Sounds like you have an open hole in the firewall that as soon as you provide an air exit path heat comes in from the engine compartment. Check the boot around the steering column and anywhere someone may have run wires through the firewall. If it were heater heat the a/c would be hot as well.

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"Without Fleet The Pride Doesn't Ride"

1983 300SD 609K + still going strong!
1970 Monte Carlo
1994 Ford F150