I think that is a good idea. My concern is the idea that the thermostat was removed when you purchased it. People usually do that because of an overheating issue.
Do what you mentioned, the flush. Here is a link that you may find helpful:
https://www.2carpros.com/articles/coolant-flush-and-refill-all-cars
Keep in mind, it isn't odd for the upper and lower radiator hoses to feel different as far as temperature. The radiator is cooling the antifreeze.
Let me know if the flush helps or if you have other questions. Also, take a look through this link. Don't be alarmed when you see the title. LOL, I want you to do a couple of checks related to a bad head gasket.
https://www.2carpros.com/articles/head-gasket-blown-test
I'm just suggesting the basic tests in the link because a blown head gasket can cause overheating as well.
Let me know what I can do to help.
Take care,
Joe
Saturday, July 10th, 2021 AT 9:19 PM