I'd elect to put a thermostat back in. Especially since you run an EFI (computerized) engine which takes into account coolant temp to adjust idle speed and engine parameters. To simplify it, as long as the engine detects that the coolant is 'too cold' it will maintain a high idle speed (wastes fuel).

Since the thermostat is out already, just buy a new one (they're not expensive) and put it in.

And while you're replacing the thermostat, drain the old fluids out and put some fresh coolant and distilled drinking water in the system.