My car heater started acting up. It would heat, then no heat. So I put a new thermostat in, had the heater core flushed, and new coolant added. The other day after this, it got so hot it shut down. I had it towed, they changed oil, and put another thermostat in, but it is still doing same thing. Help, very low funding.
Your initial approach was solid: New thermostat followed by a flush/fill.
....another simple thing you can try is replacing your radiator cap. Old radiator caps have seal erosion won't hold pressure, slowly leak coolant, and then once the coolant gets low, you'll get these symptoms--slow to heat and wild temp fluctuations.
So I think the only cheap thing left for you to try is replacing the radiator cap.
Also, you might check your coolant level a couple days (or even several hours) after you last top off the reservoir and run the engine. I've heard of radiators "burping", where it seems like they're full, then after the car runs for awhile, it's like "oh wait, but now it'll accept more coolant??" So this is just to be prudent make sure you're really starting with a full radiator.
If neither of those two tips gets you going, unfortunately this could mean a failing water pump. :/