The transmission doesn't engage once it gets hot. It also doesn't shift properly.
Unfortunately the information provided for your Jeep Grand Cherokee is general and a bit limited. It appears that the quality of the fluid in your vehicle may be dirty and I would recommend having a transmission service performed.
A transmission service entails dropping the transmission oil pan, replacing the transmission filter, resealing the transmission oil pan and adding fresh transmission fluid to the transmission. During the transmission service, the technician can visually inspect the fluid as well as the magnet inside the pan that catches metal debris from recirculating into the transmission. A large abundance of captured metal shavings will indicate excessive wear inside the transmission.
If after the service is performed, the transmission is still experiencing difficulty shifting, it will need to removed from the vehicle and taken apart to inspect for worn out components that need to be replaced.