Electronic – Could I use a surface mount thermistor to measure ambient temperature

Data & power can be sent on 2 wires without too much extra effort. This allows a microcontroller or other electronics to be placed near the sensor, as Olin suggests.
There are various ways of doing this.
You can occasionally stop powering the remote device and "deep modulate the power circuit digitally. This could be achieved by as simple a means as feeding the MC via a diode and using a reservoir cap. When you turning off power feed it detects loss of power feed and outputs signal on the line.
Or you can modulate the current draw incrementally by a small amount of DC.
Or you can have the DC feed as high impedance to AC and inject AC signal on top of the power feed.
Or ...

You may be able to scavenge power from the motor feed lines and use the final 2 wires for signalling only.

BUT you mention using a thermistor. Unless your requirements are very special you can almost certainly use a 2 wire sensor that draws a current proportional to tempeature which you then convert to voltage remotely. This is rlatively immune to line resistance variations.

As an example the AD592 - datasheet here provides temperature to current conversion, +/- 0.5K uncalibrated initial accuracy, typically +/- 0.15 K linearity (0-70C but similar elsewhere), -25 to 105C operation, relatively low self heating and 4-30V operation. Possibly the greatest issue is whether the thermal time constant meets your requirement. If this is for general ROV environment temperature measurement then this is liable to be acceptable (see data sheet). It can be used in a variety of configuration (see data sheet) with two examples shown below. If desired the top circuit (4-20 MA system) could have all the shown electronics implemented in the ROV and provide a standard 4-20 MA sensor remote signal. This signal is able to be handled by many off the shelf instruments or converters.

Even if using a thermistor, the line resistance can easily be made very small relative to the thermistor resistance so thatthe error is small. Extraneous signals induced in the line can be filtered - easily so if you thermal time constant is more than a second or so.

Edit: there are a lot of products already on the market exactly like this if you don't want to make it yourself. Look at numbers 2 through 5: http://homecooking.about.com/od/kitchenequipmentreviews/tp/electricthermom.htm

If you can get a resonant coil and thermistor system with enough SNR to reliably detect temperature remotely, then that seems to be the best solution. If not, here's some information about wireless sensor nodes.

In terms of wireless data transmission, infrared radiation of an object increases in proportion with temperature. Unfortunately, this information could only tell us the temperature of the surface of the meat, and not the center. At first I thought maybe you could use a spike with very high thermal conductivity so that you could see the temperature of the inside by looking at the spike with a thermal camera. However, the spike would just effectively cook whatever its touching so it would probably do more harm than good. For this reason, whatever design you choose to go with, the spike you insert should have very low thermal conductivity so that it doesn't cook the meat from the inside. Unless you want that.

The IR radiation coming from the oven/pan also introduces another problem: noise. You will have to select an IR transmitter with a frequency that doesn't overlap with the IR noise from the cooking implements. Maybe all IR transmitters are designed this way anyway, I don't know. Just something to be aware of. You could use an RF transmitter instead, at the cost of higher power. RF has the advantage that it will penetrate through more obstacles than IR.

A thermoelectric generator would be the most effective way to harvest energy. Because there is expected to be a large temperature difference between the outside of the meat, and the insulated inside, you could place a TEG along this gradient. But then you probably need to have a voltage regulator circuit to power your digital control circuit, temperature sensor and transmitter. I don't know if the TEG can produce the power you would need. It may be easier to just use an energy storage element like a super capacitor or chemical battery. Here is a tiny battery that operates up to 85°C: http://www.infinitepowersolutions.com/images/stories/downloads/ips_thinergy_mec225_product_data_sheet_ds1014_v1-1_final_20110913.pdf

They say, "Standard electrochemical degradation is proportional to temperature increase. Contact IPS for performance information regarding higher temperature applications up to 150°C."