@Tj
It's not just heat, it's current too. You'll need to source a pokey PSU to supply the required juice for the A1200, HDD (required to load an os containing '040 specific libraries), CPU and extra memory.
The A500's stock PSU struggled on my 25Mhz system.
On the plus side, my 25Mhz '040 was fitted with a heatsink between the fan and surface of the chip and ran happily at 40Mhz without problem. I tried maxing it to 50Mhz, but all I got was a black screen, but the system was none the worse after being reset to 40Mhz again.