My 91 4 door Sidekick did the same thing,and it ended up being stuck valves.i had the tranny flushed and cleaned,which is where an actual cleaner is run through after the old fluid is flushed out.Not just the typical tranny flush where they just remove all the old fluid and fill it wish fresh.
It works perfect now hot or cold,and has no problems.It even got rid of the annoying Extra Shift,which seems like it shifts into a 4th,non existent gear.
I also replaced my modulator valve at the time,and added Lucas tranny treatment when i refilled her with fresh fluid.
Hope this helps