does a laptop run hotter when plugged in
Yes, it can do. Have you considered dumping a can of compressed air through it, or getting the vacuum cleaner on the various cooling slots in case dust has built up on the heatsink, if any?
Does the laptop fan, if it has one, seem to behave any differently? If you try the vacuum, there's a small risk you can damage the fan.
Although you think you've used up your quota of tech fixes, it sounds to me you could claim under warranty here since your son changed drives 3 weeks ago.
