1998 Cadillac SLS so confused?

Under the dashboard on the passenger side is a Blend door Actuator, which opens and closes a door to allow hot or cold air to circulate into the passenger compartment. If that actuator does not work, the door will remain in its last position (in your case the cold air position).
You may have to remove the glove box to get to that actuator (to see if it is working). You'll also need to remove the plastic cover under the dash on that side to allow easier access.
Once located, make sure that the actuator's rotator (a round metal piece near the top of the actuator) moves are you turn the climate control from defrost to floor, to vent.
Let me know what you find.

Wanted to say thank you, that was the solution even though I had to buy a new one but it was so worth it!

Thank You so much,

Shelly1971

You're very welcome. Glad to be of assistance.