I have a 2003 chevy tahoe Lt the air works in front and with back controls but heat is only working in the front it blows with back controls but puts out no heat what causes this?

SOURCE: 2001 tahoe front heater not working, rear heater blows warm air

Notorious for plugged heater cores. Also updated plastic restriction couplers mounted at heater core available from dealer. Try back flushing heater core. Run engine till its at operating temperature then carefully hold the inlet and outlet hose breifly with heater fan on high if hoses are nearly the same temp then flow is good , if not then core is plugged.

SOURCE: 2003 chevy tahoe no rear heat

I know the earlier tahoe's have two heater lines running from the engine compartment to the rear under the vechile. Those lines could be clogged or pinched shut. What you do is get two hose locking pliers. Go under your truck, they are two metal lines that turn into rubber and back into metal again farther down the line. First, checked for pinched lines. If none, find where the rubber hoses are, clamp them off, remove from metal lines and drain. Use garden hose to flush fresh water through. When water comes through at high pressure and pretty clear, it should be done. Reconnect hoses, top off radiator fluid and it should be fine.

SOURCE: 2003 Chevy Tahoe

Its probably the temperature actuator located in the right rear interior

SOURCE: 2003 chevy silverado 1500HD LT. A/C fan works intermittently

First check fuses, then test blower motor, Last Temp control switch

SOURCE: 2005 tahoe no air blowing

as long as all the fuses are good.. its probably the blower resistor/module... located next to the blower motor under the pass. side of the dash..