2003 Hyundai Elantra I need more info please

Engine Cooling problem
2003 Hyundai Elantra 4 cyl Two Wheel Drive Automatic

now here is the problem, I have checked coolent, its fine. My mother who commutes up the cajon pass is telling me that the car is starting to overheat unless she drives on old rout 66, not as steep of a incline. She is convensed that the gadge is wrong how can I test it to make sure the gadge is reading the correct temp. And im asking because @3 monthes back had to replace thermostate housing that was cracked. Please help I dont want to worry if my mom gets stranded on the freeway.