The hose being hot is normal if the engine was just turned off or running. As far as the code, the thermostat is the likely cause. If the engine doesn't warm up fast enough because the thermostat isn't allowing it to, it increases the emissions put out by the vehicle which can result in the code you mentioned. So what you have suggested makes sense to repair the issue.
Here is a link you may find helpful. It explains in general how a thermostat is replaced.
Here are the directions specific to your vehicle. The attached pics correlate with the directions.
2005 Pontiac G6 V6-3.5L VIN 8
Vehicle Engine, Cooling and Exhaust Cooling System Thermostat Service and Repair Procedures
J38185 Hose Clamp Pliers
1. Remove the air cleaner intake duct.
2. Partially drain the cooling system.
3. Use the J38185 in order to reposition the hose clamp from the thermostat housing.
4. Remove the radiator inlet hose from the thermostat housing.
5. Remove the thermostat housing bolts.
6. Remove the thermostat housing.
7. Remove the thermostat.
8. Clean and inspect the thermostat housing gasket mating surfaces.
1. Install the thermostat.
2. Install the thermostat housing.
3. Notice: Refer to Fastener Notice in Service Precautions.
Install the thermostat housing bolts.
Tighten the bolts to 25 Nm (18 ft. lbs.).
4. Install the radiator inlet hose to the thermostat housing.
5. Use the J38185 in order to reposition and install the hose clamp to the thermostat housing.
6. Install the air cleaner intake duct.
7. Fill the cooling system.
When you refill the system, here are the directions for bleeding the air from the cooling system. Again, the attached pics correlate with the directions.
1. Notice: The procedure below must be followed. Improper coolant level could result in a low or high coolant level condition, causing engine damage.
Install the engine block left coolant drain plug.
2. Close the radiator drain plug.
3. Lower the vehicle.
4. Vehicle should be level.
5. Add a mixture of 50/50 DEX-COOL(R) antifreeze and clean drinkable water until the level stabilizes at the weld seam on the surge tank.
6. Unscrew the coolant bleed screw on the engine until coolant comes out of the bleed screw.
7. Close the bleed screw.
8. Add coolant until the level stabilizes at the weld seam on the surge tank.
9. Install the surge tank cap.
10. Important: DO NOT exceed 2,200 RPM.
Start the engine and run at 2,000 RPM until the engine cooling fans turn ON.
11. Remove the surge tank cap.
12. Refill to the weld seam on the surge tank.
13. Important: Coolant should be at the full cold mark when the system cools.
Install the surge tank cap.
14. Inspect the concentration of the engine coolant using J26568.
15. Rinse away any excess coolant from the engine and the engine compartment.
Make sure if the vehicle still has the original DexCool coolant not to mix it with the traditional Green coolant. Either use DexCool or look for a universal coolant that can be used with DexCool.
I hope this helps. Let me know if you have other questions.
Images (Click to enlarge)
Monday, November 9th, 2020 AT 7:53 PM