A working computer can't be overheated by any software, not even demanding games
I was trying to play C2C mod for civ 4 on my computer and at the same time (two monitors) watching a movie. But i think my computer can't handle both.. High temperature (around 87 degree celcius) on my cpu board.
This sounds wrong on so many levels. For a start, most hardware can't handle such temperatures. The iCore series can handle 65 °C and throttle itself down when approach that in order to reduce heat production. The PowerPC 970 (the one Apple calls G5) can handle an extreme 85 °C and Apple stopped using it due to power/heat issues. Assuming your CPU really is 87 °C, it's time to consider buying new hardware because your current setup is dying. Overheating electronics like that is a killer and annoyingly the actual death of the chip happens around 3 months after the overheating. In other words you might need a new CPU for Christmas regardless of what you do from now on.
My advice is to fix the airflow in your computer cooling. Open the computer, remove the dust and stuff from fans and heatsinks. Turn the computer on and check that all fans are spinning. When the CPU reports extreme temperatures, check that the CPU heatsink gets hot (be careful not to burn yourself). You might have a problem transferring heat from the CPU to the heatsink. Check all vents and fans in the case itself.
When my CPU fan died, my CPU didn't even reach 65 °C due to the case fan cooling. 87 °C sounds extremely hot.
There are plenty of websites about cooling computers and it isn't hard on intro level. I managed to keep the CPU below 45 °C (around 50 °C when stress testing) using nothing but low noise fans, effectively making a high end (relatively) low noise computer with nothing but off the shelf components with no custom modifications. There really is no excuse for having a computer, which gets even remotely near the temperatures you report.
I will like to know if there a good mod with more tech, units, like C2C that i could run on my computer?
C2C is likely one of the worst candidates for your needs as it has the highest requirements. However the civ4 engine is single threaded for the major workload and as such only one CPU core will get hot. In other words the civ4 engine is friendly towards heating issues.
Regardless of requirements of the game itself, running on a computer, which overheats due to CPU load is a very bad idea. You can do something simple as web browsing, enter a page with a bad script, which is stuck in a loop (it happens) and the CPU load for one core goes to 100%. Just have say 5 tabs open and the browser alone can potentially overheat the system. That's not a stable system. Background anti virus scans might be enough to trigger an overheating issue.
