Your heater problems can be caused by a "blend" door in the HVAC plenum under the dash that fails to position properly. This door is positioned by an electric servo motor controlled by the temperature selector on the HVAC control panel. If the servo motors are not working correctly or there is a problem with the rheostat of the temperature control you could have some problems with temperature control.
The other HVAC function that can cause problems is a bad vacuum motor or leaking/broken vacuum line that controls the various modes: vent, defrost, bi-level etc. If this valve does not function properly you can have temperature problems also.
I have to ask; how to you care for your Jeep? Do you treat it like a toaster or do you do the regular maintenance items on it? Because if you do treat it like a toaster, well, it's payback time.
The electrical problems could be loose or corroded ground connections. Power shutting down and then coming back would seem to point to a potential electrical problem.
Is the "Check Engine" light on?
Fix it yourself? How mechanically inclined are you, how willing are you to do the job and do you have the tools to do it? If you are going to attempt or consider doing this I would *strongly* recommend you get a copy of the factory service manual. You can download one here:
http://www.greatlakesxj.com/tech.html
Read up on the procedures and see if you can locate the items you need to potentially repair.
If this were my Jeep I would start with the electrics. Start at the battery. If it is more than three years old get a new one. Scrub and clean the battery clamps. Now, systematically go through the vehicle and check, clean and tighten all the ground points. There are some from the engine to the chassis, the transmission to the chassis and wiring bundles to the chassis/frame. There is a power distribution box in the engine bay; pop the lid and check the main connections ....the main lead from the battery and the ground lead connections. Use the service manual to locate the ground points. Also while you go through your Jeep, check for obvious loose connections, potential shorts due to abraded insulation and anything else that looks suspicious.
There is a component, called a Crank Position Sensor (CPS) that when it fails, allows the engine to crank but not to start. Now, I don't think this is part of your problem because it usually just fails ....there is no intermittent problem with it. That being said and as a firm believer in Murphy's Law you might just want to replace this thing.
Look at the service manual heating/cooling system chapter. Here is were you're going to replace parts. The manual lists the servo motors, the vacuum motors/system and the HVAC control panel as potential problem areas for malfunctions in temperature control.
Now, the fact the engine had a potential overheat; when was the last time you did anything with the cooling system? At a minimum I would do a flush and fill on the cooling system. You can either do this yourself or ring it to a local shop and have them use their machine to perform the task ...maybe $100 or so. How does the serpentine belt look? Can't remember replacing it? Time for a new one.
I'm thinking if you work the electric system and troubleshoot and repair the HVAC many, if not all, of your problems may disappear. If after doing this work and things fail to improve, then it's probably time to cry "uncle" and bring it to the dealer