Well, you have definitely built a successful rooter/cloner thats for sure. Congrats! LOL!
Yes, the heat would be caused by the
pump as submersible pumps do that.
you could probably do multiple short cycles and keep that problem down..but as a cloner/rooter, you've already have what you need for the time you've run it.
The roots like nice and healthy, definitely time to move them to a bigger unit as mentioned previously.
For the purpose of Rooting like this, the T8 will work great, but before to long they will start to get very streched out trying to get more light unless you keep the room very cool (50-55) and the
lights Very close to the plants if not Right on them.
If your going to attempt to finish them indoors, I too would recommend
hps lighting as peppers like LOTS of light and Warmth, and Florescence don't have the penetrating power to get light all the way down and around your plants to do them justice.
Now..as far as the problem with your lid leaking..you might want to check into containers that the lids drop down a little more..so you don't have water running all the way to the edge of the lid. More of a Sunken area. Not sure thats a good explanation LOL.