I used to have a small refrigerator plugged into the same circuit as my PC here at the office but it kept pulling too much juice and would create popping noises periodically. It never caused a reboot but I moved it to the other wall anyways and haven't had anymore problems. So, yes the heater is most likely the problem.
Other problems may include:
1. A virus causing reboot periodically. (Does it give you a countdown before it reboots?)
2. Your computer is not recognizing your RAM properly. (I had this problem a couple of years ago and I finally figured out that my computer was looking for RAM in a slot that it wasn't plugged into. So, when I was playing graphic-intensive games, it would need that extra memory but when it went to find it, it wasn't in the slot it thought it was which would cause a reboot. I just moved the sticks around to correct this.)
3. It could be your power supply is going out. (If you have any spare power supplies lying around, you may try to replace it.)
4. Overheating. (Mentioned earlier but can cause reboots if your computer is too dirty.)
Any of these could be the problem but I would definitely check about reconnecting your space heater to another outlet on another circuit before trying anything else as the heater is most likely the problem.