1992 Lincoln - engine starts fine but car needs push to move when cold

Will make the presumption that fluid level and condition has been checked. Will make further assumption that the fluid level has NOT been changed lately by adding fluid. If false, probably got air in there.

I dunno of any temp sensor that prevents transmission moving the vehicle in first gear when the vehicle is cold. There typically are sensors that prevent shifts into overdrive when either cold or overheated, but never heard of one that prevents movement at low temp.

Once it warms up, does the transmission shift thru all of the gears properly [including locking up the torque convertor] or does it by any chance appear to skip a gear or so.

Is reverse effective when cold?

I'm not familiar with this particular transmission, but generally the only things electronically controlled are the line pressure (shift firmness) and shifting between gears. Shifting into drive is basically just mechanical/hydraulic.

Check the fluid level first... Make sure to check it properly according to the manual (usually trans warm and engine running, but I don't know this car.)

Short of low fluid the only thing I can think of that would cause this problem would be an internal trans failure. Most likely a seal that doesn't when it is cold and then does once it warms up and gets pliable again.

Steve B.