And yes, if the unit is working properly, it will not come on until the engine temp is greater than the inside temp of the car.
Does it come on when on defrost? That will bypass the temp system.
I am thinking someone drilled holes around your t-stat, and it is taking a long time for the engine to get warm enough to turn the system on.
Could try cardboard in front of the radiator, but watch temps really close.
I read this as the unit is not comming on until you slow down. If it is on, and the air is not warm, then I would also start with the mono-valve.

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83 300SD Dark Silver Dark brown inside