If the lower hose is always cold, you most likely have one of two problems, blocked radiator or your coolant wasn't mixed right and had too much water, which allowed ice to form in the radiator or lower hose. I would recommend draining it out, preferably in a semi warm garage so nothing is near freezing, which will let you drain as much fluid out as possible. Then replace with new 50/50 premixed anti freeze. The hose from the thermostat will be hot once the engine warms up to operating temp, the lower hose should be too after that. If it's only starting to overheat after the interior heat is turned off, especially since you said the heat is so high temp, it sounds like the heater core is acting as the radiator and your actual radiator is not getting flow through it.