Bad Blend door in heating system
For a 1993 Ford Thunderbird , 5.0 liter / 302 cubic inch V8 : ( BCI group size 65 , 650 to 850 cold cranking amps )
Sounds like it is low on coolant.
Temp blend door malfunction.
A broken blower fan. Had that on my Ford Explorer. Not a big deal to have a mechanic fix it, under $200
Low refrigerant causing compressor not to start?
According to the 2004 Ford Thunderbird Owner Guide : It came from the factory with the ( Motorcraft BXT-66-650 ) battery * that's BCI group size 66 , 650 cold cranking amps
possibly low on freon or a blown fuse
She was Sandra Brennan.
It doesn't really blow it out it just warms the cold air.
Low refrigerant defective pressure switch
Your problem sounds like the common blend door problem on the Ford Expeditions, and Ford Explorer. Check related link below
90% of the time it is the temp mode door actuator located in the driverside rear of the truck