I've got a '94 with a 4L80E. It doesn't go into gear very well when I first start it up in the morning. The warmer the better it works. Now once it's up and moving it shifts fine.

I thought automatics were suppose to run worse when it heated up not when it was cool!

 

Sounds like your filter might be clogged and letting fluid flow better once it's warm.

 

The truck does have 375,000+ miles. I have no idea of the upkeep. So, I guess it couldn't hurt to change the filter and fluid.