X2 on not using the stop leak...you'll end up with clogged cores in your radiator.
As mentioned, check your T-stat and make sure you put the right O-ring on the top, otherwise you might as well not have a T-stat at all.
temp guage on a properly running 60 usually hovers just below half way at operating temp, as far as I know.
Finally, yes those two are certainly related. it doesn't take much heat from the engine to bring your coolant to it's boiling point. After that, if the system isn't pressurized (IE has a leak or a bad seal), the coolant will remain at that same temperature regardless of how hot the engine gets and simply boil/leak and not take enough heat off the engine nor deliver enough heat to your heater core, and your temp sensor will only get a reading of the coolant temp, not your engine temp. If the system is holding pressure, however, then the fluid can absorb more heat from the engine, thus saving your HG and keeping you warm (PV=nRT, temperature is proportional to pressure). Definitely fix the leak and pressure test your cooling system.