From the 3rd link that I provided:
4R44E/4R55E/5R55E COMMON PROBLEMS
Q1. My 4R/5R is starting to display an OD light that is flashing, and the shifts are sometimes late, or "soft".
A1. These transmissions use an electronic pressure control (regulator) solenoid (EPC) that works hard to maintain a contant pressure as commanded by the computer. It seems these have a useful life of 65,000 miles on the low side and about 150,000 miles on the high side. In addition, these transmissions were prone to blowing out main control (valve body) gaskets. FORD came out with a technical service bulletin (tsb) on these issues and there is a kit that modifies the VB and changes the separator plate and gaskets. I recommend whenever there is this issue to change out the EPC. It costs about $115. The FORD mods are about $30. This is a good time to upgrade the Valve body too. (See separate Q on this below).
Q2. I have a 5R55E transmission in my late 90's Explorer. I am strating to notice some shifting issues in the shifts between 1-2 and 2-3 ... kind of soft or dealyed and the RPM's will increase a little until the next gear engages. Is this serious? Is there something I should or could do to fix this?
A2. While, in fairness, there can be multiple possible causes for these symptoms, in general a majority are related to either leaking valve body (Main control) gaskets, or an Electronic Pressure Control Solenoid that is getting tired. When I hear of this problem, I generally refer folks to the 5R55E Valve Body Rebuild Diary here in the stickies, and also recommend a "shift kit".
What is a shift kit?
A Shift kit is an aftermarket engineering attempt to fix deficiencies in the original design. In many cases the actual manufacturer will pick up on some of these fixes and incorporate their own in later versions of the design. Overall, the 5R55E is a transmission with weaknesses in the Valve Body that shift kits address nicely. I recommend that if you ever have a need to remove the transmission valve body you have a shift kit installed. I think it will improve the life of your transmission.
Also, from Post #1 in the last link:
[postscript.... someone asked about computer control when things go bad. It is called limp mode. The computer will command "limp mode" when all hell breaks loose (in other words stuff just isn't seeming "right" to the computer)... It goes to a default program that maxes out pressures (to insure engagement) and uses gears designed to "get you home" As I understand it starts in 2rd and stays in 2nd or only shifts to 3rd. (Not sure about this though.) The shifts are horribly hard. Anyway there is so much to learn...
I'm no kind of expert on auto trans, but there is plenty to read in those links. Seems like either a Valve Body gasket and/or OD or EPC Solenoid issue to me. Those seem to be common trouble areas.
Throw a Shift Kit (pick one) and a couple solenoids at it.....even if you have to get JY solenoids, it'll tell you something without an expensive "rebuild", which it sounds like you do NOT need, since it shifts OK until it warms up. To me, that sounds like a solenoid giving up the ghost after it heats up.