1997 Chevy Tahoe Is engine fine or is gauge broke?

We have had a run of low temperature days (0-17 degrees) yesterday heater would blow hot then cold it correlated with engine temp gauge as the temp would go from 140 (heater worked) to 260 (heater blew cold air). I stopped at Jiffy Lube for an oil changeand told them to look at radiator fluid. They told me that when they checked it that it needed fluid and that they had added the appropriate amount. Since then the heater has worked at lower than maximum levels but acceptable and the engine gauge stays at the lowest setting. I checked the radiaror cap and even after running for twenty-five minutes it and the radiator are cool. What do think is going on and is it safe to drive?