I have a 2004 grand marquere. When I drive about 45miles per hour or lower the aircondition puts out cold air. When I get on the interstate or drive about 60miles per hour it starts blowing hot air then when i get off the interstate and slow down it starts blowing cold air again. I have had it in two shops and they cannot find anything wrong.
Does this car have manual HVAC controls (knobs) or fancy-pants electronic controls (buttons and digital display)?
I am going to suggest it is a vacuum problem. Low vacuum means the blend doors of many cars will default to the default (heat) position. You may need to find out why you have low vacuum at speed. It could be a brake problem, so you don't want to let this one go.
Joseph E.Meehan has an excellent suggestion. You can probably check this by just accelerating the car in Park, with the airconditioner on, if it begins to blow hot air, the problem could be related to vacuum.
You could also have the drive belt checked to see it starts slipping when you reach higher RPMs.
For me the best clue that there was a vacuum concern in a HVAC system. Is that when you put alot of pedal to it the air stops blowing in your face and comes out the defrost. But now vacuum controled blend door motors,have to be hard to get to. would want to verify that the blend door motor is vacuum controled. I think a better quality shop manual is called for.I have done some S-Blazer concerns and they were electricaly controled.