Why do external hard drives run so hot while mounted and idle on a Macbook Pro?
It's simple. Heat comes from the drive motors spinning - so more heat implies more time spinning. (And since these drives spin at constant rates - it's more the duty cycle that the motors are on, then how the motors are being controlled that affects heat generation.)

I will assume you have selected "Put hard disk(s) to sleep when possible." in energy saver since that needs to be checked for Mac OS X to tell the drives they are no longer needed. When they are idled the heat generation is less.

If you asked to idle the drives by selecting the choice above, then you need to find what process is polling the drives which keeps them in a non-idle status. The fs_usage command would be a great place to start to monitor what writes/reads are happening.

Once you know what processes are responsible, you have a chance to change things.

Alternatively, you can use Disk Utility to unmount the drives. They should sleep well but at the cost of not being mounted.