I think if the temperature sensor says it's too hot the transmission will go into limp mode . Since yours works cold & not warmed up I would check for a faulty temperature sensor .
Not very lickely to be the problem, because it would have set a code for that and the transmission overtemp warning would have come into view.
Also, when i´m not wrong, it will not go into limp mode for high fluid temperature.
JEEP Grand Cherokee 4.7 Lmtd 2004
HID 8000K in low and fog / Quad Squad member
KYB Gas-a-Just shocks / Pirelli Scorpion ATR 245/65/17 - Transgo reprogramming shiftkit.