Saturn Repair Problems? Ask a Mechanic for Answers ASAP
Hello and thank you for your question,If you are sure the cooling system is now full then yes, I would agree with you that you likely have a sticking and or a slow to respond thermostat especially if the car has set for a long time. I would start with changing the thermostat and while you have it drained replace the coolant with new new. Post back with the engine size if you need the replacement steps and I can send them as well.
You do not need to drain the block, draining the radiator will be enough to change the thermostat. And yes once you have replaced it refill the system with some fresh coolant and you should be okay, The thermostat should be in the lower hose but if you can gime your engine size I will double check it for you to be sure.