Also remember when it's cold, the fluid is thicker, pressure is higher. More pressure, quicker engagement of the clutch packs.
A sticking valve I would be more inclined to say would show on a hot trans. Fluid is thinner, and metal expands when heated, so tolerances will close up slightly.
Just like your oil pressure gauge reads higher when the engine is cold.
Also for S&G's check the kick down cable adjustment. If it isn't correct it can change how the trans will shift.
Easy check/adjust. Take two people. Go under the hood to the kick down or TV cable, the one beside the throttle cable. You'll see it had a clip on it, right where it goes through the bracket. It will be a lift up or push down clip.
Engage the clip, push the center section of the cable back in the housing. Now have the second person floor the throttle (engine off!) The cable will automatically extend to the proper setting. Done! it's adjusted properly.
97 Sahara, 74 Renegade, 72 CJ5, 55 Willy's (the Beast) Boss 302, 6:34 gearing, Bose 901 speakers.
God I miss that Jeep. Forgot the kinda Jeep, 80 SX4.