I have a 2001 alero olds. hose coming from themstat is hot going inside fire wall .other hose going from firewall lukewarm. change thermstat and flushed out what is the problem

Aren't there hose clamps on the two hoses at the firewall? That hose should come off right there-one is connected to the heater core inlet inside the heater case, the other hose is connected to the heater core outlet tube. While you are at it, replace both hoses. Heater hoses are standard sizes, like only two sizes, larger is 3/4 " diameter. Take an old piece of your hose to parts store for replacement. They have rolls of heater hoses, can cut you off just what you need for low price.
If the hose clamps are not on the hoses at firewall, they must be accessed from under the dash, but should be easily accessible.
Really, a 1962 falcon? 50 years old and still going? That was the year I graduated high school, driving a 1957 Dodge two door black hardtop, yes, the big finned clown car-lol.

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Your mode door (the door inside the A/C housing that determins where the air blows out) is vacuum controlled.

The MOST LIKELY cause of your problem is a broken vacuum line in the engine compartment. I cannot tell you EXACTLY where it is located because you did not mention which engine your Alero is equipped with.

Look in the area between the engine and the firewall. you will see a plastic vacuum line that goes through the fire wall. This will be the vacuum source for your HVAC system. You will most likely find a break in this line due to the extreme heat and vibration in the engine compartment. If it is found to be broken it can be "spliced" back together using a short piece of windshield washer hose.

If you find this line and it looks OK and is properly connected to the engine intake manifold, then you could have a defective mode control switch (the vacuum switch that you turn to change where the air comes out) or you could have a bad mode door or mode door actuator.

LOOK DOWN ON THE LOWER BACK ENGINE FIREWALL, LOOK AT THE AC EVAPORATOR LINE GOING TO INTO FIRE WALL. IT HAS A BLUE CAP,THATS WHERE YOU CHARGE UP THE AC SYSTEM.THAT IS LOW PRESSURE SIDE PORT.

your firewall is between your engine compartment and the inside of your vehicle so if your out side with hood popped then the wall in the back is your fire wall hope this helps good luck

Sounds like one of the connections to the heater core are leaking. Should be hoses connecting to the metal heater core pipes. The heater core is on the inside of the car with metal pipes going through the firewall to heater hoses.

Take a heater hose off and start it up, it should push it out, a lot, like 10psi pressure. Is the cooling system clean? not rusty?Does the heater blow hot air when the engine is hot, if so thats good. when the cooling fan comes on, is the air coming through the radiator hot...it should be. if not, the radiator may be stopped up. if the top and lower hoses are hot, but the air coming through the radiator is cool, the radiator is plugged, and will need to be taken apart and cleaned by a radiator shop, or better yet, replaced.

Take off the hoses at the bulkhead/firewall that go to te heater core, use a garden hose and back flush the core by forcing water through the smaller of the 2 hose nipples, if the water runs right through then you have a heater air temp control door actuator problem

When all your hoses are hot I want you to check the heater hoses near the fire wall. Are those 2 hoses equally hot? If not you may have a blocked or leaking heater core. Also make sure the flaps are moving to open the vent that allows the hot air passage to open.

pipe going to the fire wall is usualy the cabin heater. for the time being there should be 2 hoses going to the fire wall coolant in/out. remove them from the pipe on the fire wall and blank them off or if the hose is split replace them. it could be the heater core but that usualy leaks into the cab.