would a temp sensor make the transmission slip and cause it to not shift properl

Does not sound too good. Check your fluid level...But sounds like you may need transmssion. How fluid smells may tell alot.

Coolant temperature sensor does help control some torque converter and shift point. It's inexpensive part would give a shot. Part also helps computer control some fuel injection, timing and egr functions. When part malfunctions should put up a check engine light- have checked at Autozone if so. If not change your fluid and hope for best.

Check to make sure your accelerator cable isn't stuck in a faulted position under the hood or that something hasn't caught. I hit the gas once hard on one of my vehicles and the cable wedged in an awkward spot.