I have a 2003 F150 5.4liter 4x4 and when it is cold I can not get the 4x4 to engage. It is a manual shift for the transfer case not electronic. It shifts but does not activate the 4x4 when it is cold. The 4x4 does work when the temp is about 30 degrees or better. Any ideas where to start?

 

Sounds like an adjustment issue.
A contact is just making when temp is high enough and opens from shrinkage as the temp drops.
Good luck.