Yes, there is a test. A shop can put a test gage “T’d” in with your regulat sensor and measure the actual temperature. But the coolant “back[ing] into the overflow tank” tells me that the engine actually is overheating…OR the radiator cap isn’t holding pressure like it should. The cap can be tested, but for $15 you can replace it. The cap is supposed to keep the fluid pressurized at (typically) about 16 PSI (the rating is stamped on the cap). If it isn’t the engine will overheat more readily. Fluid under pressure boils at a higher temperature than fluid that is not.
Refer back to CSA’s post.
Oh, and “burping” simply means releasing an air bubble. They can get trapped in a high spot in the system, generally in a hose, and restrict flow. Cars prone to this will typically have a small valve at one of the hose’s high spots.