But if the 030 CPU was getting too hot, wouldn't it cause the A1200 to freeze or even reset?
The 030 isn't really known for overheating. It runs cooler than the 040, and I have an 040 with no cooler or fan on my BPPC and it's run for years. With even a small cooler on the 030 it shouldn't have heating problems.
Of course, using an expanded A1200 on a carpet can overheat it, but I think users are too quick to point the finger at overheating. Software is by far the best way to crash an A1200...