94 Probe transmission

I've got a 94 Ford Probe with an auto transmission. After getting stuck in snow and eventually rocking it out, the reverse gear has a problem. When engine is cold, at fast idle, the reverse gear works fine. But after the engine warms up and the idle slows, nothing happens when putting the car in reverse....but if you step on the accelerator, the vehicle then "slams" into reverse. Time for a new tranny, or is this a serviceable problem?

Thanks in advance for any help.

Welcome to Automotive Forums.
The reverse clutch is worn from rocking the car between low and reverse. It works fine when it is cold because the tranny fluid is thicker and will apply enough pressure to the reverse clutch to make it engage. When the car is warmed up the pump pressure is less and reverse won't engage unless the engine is speeded up. I think you should be thinking about getting another transmission.