As others have mentioned, you have two problems. Your fuel pump failed and needed to be replaced. This may have been caused in part by your habit of running your gas tank so low before you refill it, but will not make the car overheat. The sensor that registers how much fuel you have in the tank is located in the gas tank, along with the fuel pump. If it stopped working after the fuel pump repair, it may be the mechanic damaged it or simply forgot to reconnect an electrical connector. If it hasn't worked since before the fuel pump went out, hopefully the mechanic checked it since he had to pull the fuel tank off the car anyway to replace the pump. If the problem is indeed the fuel gauge and not the sender in the tank or wiring, the cheapest and easiest fix would probably be to get an instrument cluster from a same or similar-model vehicle from a junkyard and have it installed. I'm not sure the voltage regulator on these is even replaceable, if it is even your problem.
If you drive your car when it is overheating, you will soon have a much more expensive repair--an engine rebuild or replacement. You are wise to stop and let it cool as you are doing, but it's still putting a strain on the engine.
I'd suggest taking it to a good independent mechanic or shop and NOT the dealer. A dealer is not necessary for these types of repairs and a dealer will charge you hundreds of dollars more and not necessarily do any better of a job. Instead of throwing more money at it, I'd have the shop do some diagnostics. (with the exception of the thermostat you're having replaced---that's a good place to start when a car is overheating) I hope it fixed your problem. Good luck.