If the heater output has gradually been getting colder, and when you turn blower speed to lowest level, the output gets warmer, AND you're pretty sure the blend door is operating properly...then the core is probably full of crud on the source side of the tubes and you probably can fix the problem by simply reverse flushing it.

99 Bravada - With above symptoms but Clean clear coolant in radiator and bottle, recent LIM gasket replace.

I went to HDW store Bought one foot ea of 5/8 and 3/4 heater hose and plastic plugs for each.
Released all holding hardware for hoses and wiring draped over the hoses to allow lifting hoses.
Disconnected three wiring connectors and moved harness aside.
Release any pressure in radiator, replace /tighten cap. This prevent 'gush' from hose nipples providing radiator is full.
Removed 5/8 hose at water pump, quickly slip short plugged piece on water pump nipple to prevent too much coolant loss.
Lift end of hose.
Did same with 3/4 hose at intake manifold nipple.
Point open end of 3/4 hose down along inner fender to avoid too much mess. Apply water hose or compressed air to 5/8 hose {water pump end}

I didnt want to screw with running water hose, so I tried the compressed air and it worked. The liquid blowing out of the 3/4 {source} end really looked like crap so I knew that a lot of crud was built up, perhaps debris from the LIM gasket replace.
Reinstalled everything and started car. Pleased that temp ga wasnt even up to 100 and got warm air out at full blower speed.

good Luck