Electronic – the exact type of oil used in immersion cooling of electronic devices such as processors

Feel free to skim read, or skip to the end. I realise I did go on a bit!

Generally you wouldn't use a soft processor to replace DSP stuff. Dedicated hardware can generally handle higher volumes of data faster because you would design it to do a specific task very well, rather than being a general purpose CPU.

Where soft processors come into their element is control and coordination.

If you were to design a system which needed to process a large volume of data, lets say high frame rate image acquisition, it would not be possible to use a soft-core processor to handle all the data, there would simply be too much overhead in the CPU. What you would do is design dedicated firmware to do the specific acquisition task needed (e.g. filter the data, store to memory, etc.).

However you still need some way of instructing it when to do things - when do you want to be capturing, has the device been instructed to offload the data, etc. These things are not very easy to do in dedicated hardware, not if there are sequences of events with user input, basically tasks which do not do the same thing over and over again. In this case you would use a soft-core processor as it is far easier to write procedural code for some tasks.

Another (real) example, I have been working on a ultrasound acquisition system which streams data via PCIe. The tasks it does are communicated from the user and various parts of the system need configuring. The coordination of the system does not require large volumes of data, but instead needs flexibility, so it is well suited to a soft-core CPU programmed with in this case C. To do the same thing in physical hardware would require vast amounts of resources most of which would be used infrequently so would see no benefit compared to a CPU.

It's worth noting that some tasks may vary depending on user input, but are still better in dedicated hardware. In fact one part of the code (programming DMA controllers to store data on trigger) was originally done in the CPU in about 15 lines of code, but because that bit needs to be done the moment a trigger occurs, using a CPU which may be busy with other stuff is not ideal. The task is instead programmed into a Verilog module, but in the process becomes a massive 500 line state machine with about 15 states and a whole heap load of supporting logic - no really. But even though it uses up far more resources, it is time critical, so is a necessity.

Similarly I need clock cycle accurate trigger generation, so a module for performing that task is part of the system rather than doing it in a CPU. Both this core and the one above are examples of how you can use a CPU to do some tasks, but for other critical ones you can develop hardware to complement the CPU - in the same way you have timers, etc. in a microcontroller.

So to summarise:

FPGAs are great flexible tools, but most designs need a combination of soft-core CPUs, configurable modules (e.g. timers), and dedicated single-task hardware.

CPUs are great for user interaction, controlling the order of events, configuring controllers. They are like the coordinator, the brain.

Some designs may need to do some fairly repetitive tasks which can be configured to suit different inputs - timer modules, character displays, button debouncing, etc. These could easily be done with a CPU, but if you want to do several of them accurately at once it becomes more tricky - they are sharing the same CPU resources. So what you can do is move them into dedicated hardware which is closely connected to the CPU - give the CPU chance to do other tasks. These help the CPU do its job and interact with its surroundings, like its senses.

Dedicated DSP, data transfer (DMA) - basically any task which will do the same thing over and over again at high speeds - can really benefit from dedicated logic in terms of speed, and also possibly power. These are like the muscles of the device, the do all the heavy lifting.

You'll have to excuse the rambling on a bit, but I do like this field of EE. Hopefully the above is understandable and gives you some extra insight to the wonderful world of FPGAs.

1. My peltier plate only stays cool for about a minute or so then begins to heat up, I'm not sure if this is supposed to happen or maybe I should lower the voltage I'm using?

This is normal behavior, your elements are not ideal, they have some resistance, and the amount of current they drain, the \$P=RI^2\$ becomes pretty high. Note that the equation says current squared.

A solution to this is to add a heatsink and a fan. With just a heatsink it will still heat up to pretty high temperatures. A fan is definitely required.

2. What would the optimal circumstances be to maximize cooling performance? Is there an specific voltage or condition that would allow a for the highest yielding cooling effect?

A heatsink + a fan on the hot side will lower the warm side's temperature. This in turn will lower the cold side's temperature further.

Some X voltage will give some Y temperature difference between the warm side and cold side. I'm not sure if it's linear or quadratic, or something else, but what I do know is this, higher voltage will increase some temperature difference, I just don't know by how much. Since you want to get very cold temperature, then you would need some higher voltage. I have no idea how much. This in turn will make the peltier heat up because of the non-ideal resistance inside of it as I mentioned earlier. So you will need an even larger heatsink and stronger fan.

Look at a computer fan that is meant to dissipate about a 100 W CPU, it's not that big, it is however pretty noisy. Which is something you will have to live with, or get a 100 cm X 100 cm heatsink or some other silly size.

3. Lastly, I was wondering is there any way to orientate the conductors to have the hot and cold plates be on the same side?

You can get several peltiers and then have some upside down and some not upside down. This will give you hot and cold plates on the same side. I believe there are peltiers in the 1x1 cm² range. But I don't believe there's much you can do on your own with that peltier in front of you. Unless you desolder one entire side, desolder the ones you want to flip, solder back, solder back the entire side. This "sounds" easy but I would never attempt at doing it. If you wonder why you need to flip it, then it's because at the junction, aka where one part meets another part, there's two different metals. And you need to switch these two metals around. Either way, I recommend that you just buy smaller peltiers and flip them module by module.

The ones you do flip will get really warm though. If you will get, say 30 °C temperature difference between the sides on one peltier and ambient temperature is 25 °C. And the temperature rise is 5 °C because of the peltier heating up due to non-ideal resistances. Then you will have 30 °C on the heatsink and 0 °C on the cold side, just barely able to freeze water. (I've done this in real life, was very fun). If you flip one of the sides you will get a little bit less than 30°C on the heatsink (because now one is cooling it) and 60 °C on the warm side. The total difference between these two sides will be roughly 60 °C. Depending on what you will be working on, that's a lot. But it's a good thing to know.

Reversing the current on a peltier will make the hot side the cold side and cold side the hot side. No problem at all.

TL;DR

Just get a heatsink and a fan. If you want to go even cooler, then get another fan and a larger heatsink and increase the voltage going to the peltier.