I have a 2005 impala it blows cold air only.the thermostate is set at the hottest setting.i dont think its the heater core because it does not overheat and its not leaking antifreeze.what could it be?

Are the water hoses to the core get warm? Are they both the same temperature? Is there a vacuum leak going to the heater controls? Is the blend door operating? Check all these points and there will be one of them that will fix the problem.

check to make sure the blend door is changing from cold to hot. With the engine off and the key in the run position set the blower motor to the highest speed. Turn the temp dial to full cold and wait 30 seconds. Now turn the temp dial to full hot a listen carefully. You should hear a difference in sounds as the blend door sweeps through its full range.

If it is working and the engine is fully warmed up feel the heater hoses where the pass through the fire wall. One should be very hot and the other should be pretty warm. If one is hot and one is significantly cooler than either the heater core is plugged or there is air in the heater core causing a block in flow.

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there are 2 heater hoses going to the heater core one has a tap or valve to regulate the water flow, this may be jammed closed or the control cable has come off. also check the thermostat if the engine is running cold.

need to make sure you have enough coolant and if it does then it could be your thermostate or clogged heater core

usually if the core goes bad it fogs things up and stinks bad'

check ur passanger side floor board. u may have a heater core out. if that's not out then u have a leak somewhere.

Get the heater core flushed if youy can verify that the valve in the upper heater hose moves when you go from hot to cold.

There's probably a little vacuum actuated valve in one of the hoses going from the engine block to the heater core. make sure this valve is working.

Also... check coolant level

and

Your water pump may be marginal, only circulating adequate collant at engine speeds above 1000 RPM or so.

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.

I have the same problem with my 2001 Tahoe. The front blower is working, its blowing strong, but its cold air even with the temp setting as high as it can get. The rear blows hot air. The engine temp guage is at about 210ish which is close to being normal (220). I just replaced the thermostate a few months ago, I don't know if its bad again, or it I deluted the antifreeze too much and it frooze the heater core, or if the heater core just went bad. Any one know what the cause could be?