Hello
The first place to start is to check the fluid it should be clean (pinkish to red in color) no debris and no burnt smell, If it smells burnt you should have the transmission pan removed and inspected for foreign material and debris, if debris or foreign material is found in the pan the transmission will need repair (internal), since you have no codes hopefully this will not be the case
Next is to check the kick down linkage at the transmission to be sure that it is free moving and does not bind or hang up ( the ball and socket do rust and the shaft into the valve body may also rust) after the check, the cable will need to be checked for free movement also and then be properly adjusted, if not found to be binding.
If both of the above are good, the transmission may need to be overhauled, what happens to these transmissions over time is that the seals inside of the transmission harden up over time and hang up the clutch piston in its bore causing a delayed and hard shift, this is normally made worse in the cold and gets better as the whether warms up, or may seem slightly better as the jeep reaches operating temp,another tell tale that this may be what is starting to happen is when it starts to hang up and not shift ease off the gas and see if it shifts, this allows governor pressure to overcome the hanging seal and make the shift, (I drove my truck like this for two years, you have already discovered this), but eventually the seal will fail completely and you will loose second and/or third gear
I hope that this helps you
If you need more information or help just let me know
Thank you
Donny
there is a governor pressure transducer and solenoid that can be a problem, but they almost always set a code and turn on the check engine light, also they would cause the transmission to go into what is called "limp in " mode, you would only have second gear and reverse, just about any electronic problem with the transmission will at the least make the check engine light come on let me know what you find with the kick down
I hope that is all it needs they should be able to adjust the bands for you in about an 1 1/2 to 2 hours, Not a very big job and not very comon unless you have a very large amount of milage
The front (kickdown) band adjusting screw is located on the left side of the transmission case above the manual valve and throttle valve levers.
CAUTION: If Adapter C-3705 is needed to reach the adjusting screw, tighten the screw to only (47-50 in. lbs.) torque.
The transmission oil pan must be removed for access to the rear band adjusting screw.
2 - FRONT BAND ADJUSTER
ASE Certified Technician
A.S.E. Master Technician, Over 25 years working in Chrysler dealers, Top tech DaimlerChrysler 1998