How do i behave with a guy who might potentially be trying to keep me warm?

You ignore it and keep trucking on! My ex did this after we broke up (blowing up my social media feeds, asking to hang out then bailing, etc), and the best thing I did was ignore it because I'd known her long enough to know it was going nowhere.

He wants to reach out he can, but you're not obligated to do anything. His actions will speak louder than his words. Stay your ground until you have something more concrete!