Heater blowing luke warm air?

The first thing I would check is the coolant level. IT must be full.

IF full, leave blower off and bring to operating temp.,
Then turn on blower to high, Is it warmer and then quickly cools off? PArtially plugged heater core.
feel the heater hoses when at operating temp. Are both hot?

This guide can help

https://www.2carpros.com/articles/car-heater-not-working

If it is slow to come to temperature and your fuel mileage is worse, the thermostat may be defective.

Check to see if your actuators on your heater are working correctly. One controls air temp and another movement. Pic enclosed of blend door

Check and test the thermostat and heater core if its clogged.

This guide should help us.

https://www.2carpros.com/articles/car-heater-not-working

Please run down this guide and report back.

With the vehicle warm and idling pop the hood and feel the heater core hoses.

Post back what you find, feel them directly at the firewall.

Is one of the hoses hot and one cold?
Both warm?
Both hot?
Neither hot?

One warm and one cold?

Typically if it is a thermostat, you'll have a much longer warm up period that could be bad enough to set the CEL. After a while you should get some heat. The gauge would also be showing cold for the majority of the time.

Low coolant can do this.

A plugged heater core can do this.
Did they check for the temperature of the hoses going in and coming out of it?

Is the pump leaking or are they assumming the impellers are worn causing a lack of circulation?

IF the coolant is full and the engine is at operating temp. Then by reving the motor to increase flow, some heat should come out I would expect if it is the waterpump.

I would ask them that if it didn't fix it, will they absorb the cost?

Waterpumps often have a lifetime warranty if it is a new one.

Very interesting. Here in the middle of Wisconsin we have a bunch of very reputable new-car dealers, and two well-known crooks. One is the local Chevy dealer and one is an independent repair shop. Those two stay in business by constantly looking for new customers. I worked for a very nice family that owns four Chrysler dealerships. We traded service manuals with the GMC dealer down the road and what used to be a pretty nice Ford dealership until the crook bought them out. We had a nice import dealer too. We did a lot or repairs on each others trade-in cars.

Also, three of my top students were girls, and the guys had a lot of respect for them. It's common around here to find lady mechanics.

For your problem, start by feeling the radiator hose after the engine is warmed up. It should be too hot to hold onto for very long. If it is not, suspect the thermostat. If it is, feel the two heater hoses. If they're cool, the heater core could be plugged, but first look for a water control valve that isn't opening. If the heater core is plugged, those can usually be cleared by running water through them from a garden hose.

You may not have a water valve, but if you do, it's inline with one of the heater hoses. Years ago they had a cable running to them from the controls on the dash. Today they're run by a vacuum motor and will have a small vacuum hose going to it.

If the heater hoses are just as hot as the radiator hose, coolant is circulating through the heater core, and the temperature door in the heater box is suspect. Look for a cable from the temperature lever that is slipping on the door's lever, or a vacuum hose that is disconnected or leaking.

The temperature door can be rusted in the "cold" position too. That's when a cable-operated lever seems to work, but actually where that cable connects to the door's lever is supposed to slide somewhat freely. That is the self-adjusting feature, but when the door is stuck, the cable slides back and forth in the adjustment without moving the door. This problem usually shows up in winter after the door has been in the "cold" position all summer and had a chance for the metal hinge pin to rust.

If the heater hoses are not as hot as the radiator hose, the heater core could be plugged. To clear it, remove one of the heater hoses from the engine, and the radiator cap, then run water into the hose from a garden hose. If the water doesn't flow freely after a few seconds, it may be necessary to remove the other hose and run the water the other way.

With the engine at full operating temp, locate the 2 heater hoses where they go into the firewall and feel them to see if they are both hot to the touch. If not too hot to hold, then you have to look at the actual engine temp and if that is up, if it is, then your looking at a restricted heater core.
If you find that they are both too hot to hold, then the heat in that vehicle is controlled by a blend door that regulates heated air flow. It is operated by an electric motor/actuator. The problem can be that the actuator is stripped or inoperative or the door itself could be damaged. This is what needs to be determined by examining the actuator and see if it is responding to heat change commands or not.
If they are both not too hot to hold on to, then you either have a restricted heater core or the system is not completely full and getting air pockets for some reason.

Any visible steam near the heads? Or white smoke out the tailpipe? If so get a block test kit, they run about 50.00, this will check for a cracked head or blown head gasket. Also make sure the tstat is in right, the copper spring should point to block!