This started as a comment but it really is an answer:
You seem to have far more code than is necessary for debugging a basic hardware function. You should be first attempting to be sure you know how to operate the IC correctly. Asking people to wade through and debug code which adds layers on top of basic functionality is a far harder way of doing things. So -
Simplify what you are doing to the the bare minimum so you are
Only once you are sure of this should you add layers of complexity.
It's reasonably likely that you are doing something wrong in the processing rather than basic data inputing. Your code needs to address the minimum possible hardware interaction needed to obtain the core signals.
Looking at your photo, you seem to have +Vs of the LM35 connected to +5V on the Arduino, so if you are reading 3.84V there, that is definitely a problem to address before trying to fix anything else.
The likely problem is this: Te 7 segment displays (or some wiring fault on the breadboard) is drawing too much current from the Arduino, and ultimately from the USB connector. This means that the voltage regulation provided by the USB power supply is no longer working effectively, and so the supply voltage that you measured as 3.84V is likely wandering, and in any case low.
While many if not all the chips in this project will operate off voltages lower than the 5V that V+ is supposed to be at, there are some aspects that will be sensitive to lower V+.
One notable V+ -sensitive feature is the A-to-D convertor in the Atmega328. (As The Photon commented.) The convertor can be set to choose between a couple of different reference voltages. Your code indicates that you have it set to use the V+ (VCC) value (5V) as the reference. If that reference is low (eg: 3.8V) then your input voltage from the LM35 will measure as a number that is scaled up accordingly.
And I'm fairly certain that if your V+ is low, it will change according to how many LEDs are illuminated and drawing current, so your measurements will vary according to what digits are displaying, and vice versa, of course.
Once you've fixed the power supply issue, you might assess whether to set the A/D convertor to use the built-in 1.1V reference instead, as this will give you higher resolution and more stable converted values. See the Atmega328 docs for more details on the A/D convertor and options.
Best Answer
I agree that thermocouples sound like the best sensors.
Take a look at some of the delta-sigma converters. In one recent design I was able to read thermocouples without any amplification. That's useful since the input offset voltage of a amp can be significant compared to a thermocouple's output voltage. I did add a FET to each input to effectively short it together so that the software could do auto-zero. You will also need a regular temperature sensor on the board because thermocouples only give you relative temperature, not absolute. You need absolute on your board to compute the absolute temperature in the oven. This may sound more complicated than it is.
I would be careful about casting things in concrete. Metal has a way of deteriorating, particularly at high temperature. I think it would be a good idea to allow for replacing the thermocouples and their leads. Maybe you can cast a small conduit in concrete instead of the wires directly. That way you can change the wires thru the conduit while the conduit (just a small pipe) stays in place.
As for getting the data back to the house, it would be useful to know how far that really is. Since this is a one-off and apparently all on your own property, I wouldn't get too worried about your local RF regulations. You can use a fixed directional antenna at both the oven and the house to get longer distance. WiFi sucks a lot of power and will give you much higher data rate than you need, although it would be convenient to connect to on the house side. The oven can be a TCP server that the computer in the house checks in with.
802.15 radios sound more appropriate, although again we need to know the distance. As I said before, two directional antennas would greatly increase distance and chance of anyone else noticing your signal. The Microchip MiWi protocol sounds like it would be a good choice for this. The data rate is low, but that's fine for this application. The nice part is that it's low power and you can shut down the oven side completely between transmissions, with the house side always on because it has much more power available. The drawback is that you then need a MiWi to ethernet bridge, but that's not all that hard.
We're actually working on distributed MiWi modules with a wall-powered base station that reports the collected data over ethernet via a custom TCP server. We've got things mostly working, but haven't released the code or the units yet. The code will be available for free when we do.