Heater Problem

[Elvis]

I have a '67 coupe with A/C and am having trouble getting heat - yes, it cools off in Texas. The hose that goes to the water control valve gets hot. The water control valve opens - at least it shows that it is open - but the hose that goes from the valve into heater case stays cool and the return hose also stays cool. It seems to me that heater core problems usually result in a leak. Could the core be blocked? It appears to me that the bottom half of the case that houses the core would slide right out if I disconnected the two hoses at the fire wall. Is this correct? Thanks for any help. E.