The lower hose will run significantly cooler than the others, as the coolant is returning to the engine, from the radiator. If the gauge shows full temperature, this is normal. If not, the thermostat is bypassing internally.
The heater almost always fails to work for one of two reasons. Either the core is stopped up, which is very common or the blend door actuator is not directing air through the core. We have had good luck clearing the cores. A guy in the shop built a tool using a combination of water and low pressure air, that works well.