The heater matrix remains hot all the time the cooling system is hot, thats normal...
The temp control slider on the dash, via cable, opens a vent on the box that contains the matrix
The direction control slider, operates flaps in the ducting, after it has passed through the heater box that contains the matrix
Sometimes the cables can get hooked up on themselves, and simply bind up, or the retaining clips on the cables can break, if someone has previously been heavy handed, cables should also fall into place, and be obvious where they fit
The bypass valves are temperamental, and can be discarded if a later quality matrix has been fitted. They were fitted after sale, because of a batch of faulty matrix's were fitted by the factory, and in very few cases, were known to dump hot water into the passenger footwell, my personal opinion is that they are more trouble than they're worth, and can be discarded, but the owner has to make that call!
So, if hot air supply is intermittent, then its likely to be the valves. If there is no hot air at all, its likely to be the flap stuck in the closed position... Or both!
Thom