You are correct, if the thermostat is stuck in the opened position, then your heater may take forever to get warm.
One thing you may want to do before you go with a new thermostat. is to simply allow the engine to reach it's operating temp and feel the heater hoses where they enter the heater core at the firewall. Both hose should be very hot to the touch.
Here's a location: This graphic only shows one of the hoses.
Notice: The thermostat will not function correctly once it is contacted by oil. If oil is found in the cooling system, it must be flushed and the thermostat replaced.
Remove the thermostat housing to water pump feed pipe bolts.
Remove the thermostat housing to water pump feed pipe.
I hope this information helps.