No, just replace the radiator. The other one (in the front) is the condenser for the a/c system.
If your heater core wasn't leaking at the time your radiator was replaced , then ( no ) That would be two separate jobs
Well, we'd need to know exactly what's wrong with it in order to answer the question. Replacing the motor and replacing cracked glass are going to be two wholly separate processes.
Follow the upper rad hose to the engine and it is in the housing there. When replacing it make sure the spring goes toward the engine. In a 2.2L engine the thermostat is inside the lower radiator hose. Where the lower radiator hose attaches to the engine there's a metal housing. Undo the two bolts and separate the two halves of the housing, the thermostat is inside.
If you have a threaded cap on your coolant reservoir that is your " radiator cap "
In order to drain the radiator on a 2004 Pontiac GTO it is necessary to pull the lower radiator hose off. There is not a separate drain plug on this radiator.
Separate the tranny and engine...It's in there.
The thermostat is located in a housing separate from the engine. It is inline with the lower radiator hose between the radiator and engine on the driver's side.
Vehicles with an automatic transmission may have lines that carry transmission fluid from the transmission to a separate tank on the bottom of the radiator.
Transmission cooler is a separate tank area attached to the lower or side of radiator (one unit)
Oil can't "back-up" into the coolant, they run in separate systems... you wasted money on the radiator, the thermostat is irrellivent, your engine block is probably cracked although it could be a gasket or loose bolts... you need a good mechanic and money
There are two separate sensors that play here. the "coolant temperature sensor" and "coolant LEVEL sensor". I suggest confirming which of these was replaced, as it is very common for them to be confused. likely you will find the coolant sensor that was replaced was the one on the engine (temperature); The LEVEL sensor is mounted either in the coolant resivoir or in the radiator. Probably just need the proper sensor replaced.
Most transmissions are cooled using separate tubs in your radiator, if this tube develops a leak it could mix with your antifreeze, you need a new radiator...