Your description is not very clear or complete. Does it get third when you tip out of the throttle all the time but not when you are on the throttle? Or never gets third? Does it have reverse all the time? Or no reverse? If you have reverse and get third on tip out - check the throttle kick down cable for freeness. There should be a return spring from the throttle lever to a bracket at the trans end. Check and make sure this cable goes wide open then returns all the way forward before doing anything else.
Shifts fine when cold, 1st, 2nd, 3rd, OD. When warm takes awhile and about 2500 rpms before it shifts to 3rd. Reverse is fine. If I lift off the throttle it usually go into 3rd. I will check the throttle cable. Yes, return spring is intact.