In cold weather, my engine temperature drops and then the transmission downshift

Thank you so much . . I never even put the heat on in the car as that makes the problem so much worse . . I doubled my gas expense on a holiday trip due to this issue . . it is the same on both of my toyota corolla station wagons . . I have another question . .the same car is stalling upon deceleration . . I had new plugs, distributor and fuel pump put on, but I have the problem again after a few days of it running just great . . any thoughts? Thank you again, Elizabeth