2001 3.1 TD auto box sticking in limp mode when cold

Nope, they didn't know what a limp mode was back in 88. You might try running an additive through for a bit, then doing a filter and fluid change, but those early ones were fully mechanical exept for the lockup on the converter.

Odometer or ABS?

crankshaft sensor maybe ?

you need to change the oil in the auto box. if this dont help then the servo in the auto box is sticking.

Have the computer scanned for trouble codes. It sounds like the computer is putting the car into "limp in" mode. The diagnostic codes should lead you to the problem.

Sticking in 2nd. Its in limp mode. You need to have the tcm scanned for codes to see why the TCM is locking the trans in limp.

without a dtc to help,the only thing you can do is check all the connections at the transmission,and unhook the battery for awhile or get check code cleared and see if it reapperars

i suspect the modulator might be faulty and mayby
trans. filter would need replacement

If the actual gear stick is hard to move you will find the linkages are stuck on something, if it moves freely and still doesnt change theres two things it could be, first is motor was incorrectly installed or second is the gearbox has gone into limp mode, limp mode is a factory set mode that keeps the car in 3rd gear for a 3 speed or 4th in a 4 speed, in the ba's i had this problem with my car, limp mode is only a safety measure to get you home and should be looked at immediatley.

depending on the year of the vehicle most manufactures not all have a specific type of fluid for the transmission. newer ones( what year is the vehicle?) this could be a sitcking valve in the valve body or a broken 2-3 valve spring in the valve body of your transmission, or a broken servo spring.