Yes, obviously doing a lot of work will cause its processor to heat up. For example, running a P2P client, especially if you’ve got firewall rules and such set up in the router, will probably cause it to work overtime and eventually heat up.
Also, yes, having wireless devices will add some heat (after all, the radio waves are radiation), but generally it is not noticeable like you described.
What could be happening is that the router has a bug and a specific set of circumstances has caused it to create an endless loop in a thread or some such that is overloading the CPU. That would explain why resetting it caused it to cool down since the block of code that it was stuck in is no longer being executed.
Consider checking to see if there is a firmware update for it (the latest one is Ver.1.0.04 (build 7); I don’t know what is in your specific router at the moment).
A quick check of the support for the router finds no mentions of excessive heat, so you may also want to consider using one of the options on that page to contact Linksys to report it; maybe it is an as-yet undiscovered bug.