I don't have specific knowledge of the Grand Cherokee, but heres how I would do it.
The thermostat restricts the flow of coolant circulating to the radiator whilst the motor is still warming up. It is located in the waterline between the cylinder head and the radiator.
Here is where I break into this answer (giant167).
On the 4.7L v-8, the thermostat is located on the bottom left of the engine block. You must drain the radiator and remove the bottom hose to access the thermostat housing.
Mr. Wheeldon continues now.
You might want to loosen the bottom radiator hose clip to drain out and save about 4 pints of the coolant before you start. Look at the top of the radiator and find a large diameter rubber hose headed towards the motor. It should terminate at a dome-shaped housing at one end of the top of the motor. There will be three or more bolts securing the housing. Remove the housing being careful not to damage the paper gasket that seals the housing and hook out the old thermostat. Replace it with one of the same type and temperature rating, making sure it is the same way up. Either replace the gasket or use some gasket past to seal the joint when you replace the housing. Don't over-tighten the bolts. Make sure all the hose clips are secure, then replace the coolant and top it up to the correct level.
Changing a thermostat on a 1995 Jeep Cherokee is very easy to do. The thermostat has two bolts holding it in place. Take the bolts off and remove the thermostat from the casing and replace with a new one.
http://www.wjjeeps.com/service/cooling.htm#THERM
Yes, a Cherokee has a thermostat.
The thermostat on a 1996 Jeep Grand Cherokee 5.2L is replaced by draining the coolant and disconnecting the radiator hose. The housing is then unbolted, the thermostat removed, and a new unit put in its place.
The thermostat on a 4.7L is under the housing where the lower radiator hose attaches to the engine.
The thermostat on a 1996 Jeep Cherokee is under the housing where the upper radiator hose attaches to the engine.
On a Jeep Grand Cherokee v6, the thermostat is located in the thermostat housing. The housing can be easily located by following the upper radiator hose to it.
Thermostat sticking. Replace thermostat and gasket.
There wasn't a 2003 Cherokee. The last Cherokee was 2000.
You need to replace the thermostat and flush the system of crud.
The 2003 Jeep Grand-Cherokee has 12 valves.
The 2003 Jeep Grand-Cherokee has a 4-speed automatic.