It is normal for our trucks not to shift out of 2nd gear until the engine reaches approximately 120 degrees, it's an emissions things and is totally normal.
Noonan, you said your truck will not shift out of 1st gear until it warms up after a few minutes, that is not normal and exactly what happened to my truck.
Give us some more history on your truck (year, mileage, tranny service history etc). Also, when it is stuck in 1st on a cold start up, have you tried manually shifting through the gears to see if it will shift? There is even a procedure in the FSM where you disconnect the solenoid plugs on the outside of the tranny and then try driving it again (cold start up like normal). If it shifts when you manually go through the gears, then its a problem with a solenoid or the valve body (won't always throw a code).
Unfortunately, I tried everything to fix mine and but ultimately had to put a different transmission in it. I cannot say for certain what caused it but I think the pump may have been on its way out. Oh and btw, my bad tranny once it was warmed up would work perfect. No slipping, harsh shifting or anything other than the stuck in 1st gear until it warmed up for a while. It did get progressively worse as the weeks went by (took longer and longer before it would finally shift out of 1st).
About a month prior to the stuck in 1st shifting problem, my truck would make a whine on start up almost like a PS whine. After about 30 seconds, it would go away. Eventually I figured out it was coming from my tranny. I dropped the pan and found that the filter was completely plugged up with a brown clay like sludge. Once I cleaned the filter, the whine never came back but I think it damaged the pump in the process.
The sludge was most likely broken down clutch pack material from when I got a pink milk shake in my tranny (coolant breaks down the clutch material and destroys the tranny). I did my best to flush it out after the PMS but the damage was already done. The transmission lasted about 12k miles before I got the whine and ultimately the stuck in 1st symptom. I tried everything from snake oil to new solenoids but the tranny was toast.
Lets hope yours is something simple like your fluid level is low (BTW, check that).