So, our microcontroller seems to heat up really quickly. What are the main reasons for why this happens?

The reason that the microcontroller heats up is electrical resistance in the wires. There is nothing that you can do about the cause, but you can help alleviate the symptoms. Don’t keep your microcontroller in an enclosed space with no ventilation when it is running for long periods of time. The VEXNet keys have been known to heat up quite a bit, so make sure that nothing is smothering the key either.

Are you sure it’s the microcontroller heating up and not the motors? Motor overheating is the much more common issue.

The one time we’ve had microcontroller heating up, we determined that there was a short somewhere in the circuit. To test, unplug all of the motors and sensors, and plug them back in one by one and see if it starts heating up. In our case, there was a short in one of the bumper switches, and we opened it up and fixed it.

NOTE that this is for really really really heating up, not just the normal heat buildup that magicode describes above.

After feeling the microcontroller, it seems that it heats up the most at the bottom, right below the digital sensors, around ports 10-12.
BTW, it is a Cortex, in case that helps understand the problem.

Is anything plugged into those digital ports? Or the digital ports at all? Try unplugging everything and see if it still happens.