I have a 1998 Oldsmobile Intrigue Gl with Automatic Transmission problems ?

On mine it only starts to give problems when the motor/transmission gets hot from driving for awhile, when it starts to give problems it will only give problems at lower speeds from 0-46mph then its fine after that. when it does it at lower speeds it acts like it wants to give out or like its having problems shifting or something like that and when it does shift it shifts hard especially when it shifts around 45mph. most of the time if i take off slow enough and slowly get up to speed until i pass 45-48 then i can accelerate faster and its fine. Other time i have to drive it like a standard going from the lowest gear, from 1st, 2nd, 3rd, and then back into drive its not perfect shifting doing this but its better than not doing it like that and the worst part of it is around 20-25mph or so and when it shifts at about 45mph but like i said it only does this when the motor/transmission is hot from driving for awhile. I live about an hour South from Wichita, KS and it will start doing it if i go up to Wichita, KS for about 10-20min and then back. it starts acting up on the way back from Wichita, KS any one have any ideas what this might be and any solutions. Im thinking it may be the one of the Transmission Control Solenoids i looked it up and it shows a few different kinds. if u think it is one of these let me know and if its not let me know wat u think so i can look it up and see how much it is so i can try to save up for it thanks for any replies u guys give me i appreciate it