The second question is easy to answer. The ATmega is a microcontroller, which is hard-wired to reboot and resume after a loss of power. In fact, that's what the reset button actually does on some boards. Many voltage regulators have an enable pin, and it's very easy to wire it up in such a way that the reset button actually cuts power to the board. Every time you apply power, the controller reads the content at 0x00 (usually a jump instruction), and begins executing code.
The first question, not so much. Lightning strikes are pretty serious events, and (especially without a schematic), it's hard to say what will happen. I'd suggest that you first provide some isolation for your circuitry. A little optoisolator is likely to provide the isolation you need, but you'll need to provide power on the high-voltage side. An easier method would be to make the temp sensor completely independent. A little MSP430 + MRF24J40 system could run for months on a couple batteries and cost less than $10, transmitting the current temperature every couple minutes. Then, when lighting strikes, there won't be an easy path to ground through the sensing wire, which means that lightning is likely to strike elsewhere instead. The easiest method (also the least likely to survive a strike) would be to place a zener diode across the thermistor. You'll want to be careful about compensating your measurements for leakage currents through the zener, though.
If you can't accept the possibility that the temp sensor would be destroyed by a lightning strike (which is an interesting requirement to design for), you should research transient voltage suppression diodes and be prepared for some much higher system costs.