The GTL really needs the thermostat - it would never get warm if the big aluminium radiator was set to work cooling down the tiny heat generated by the low power engine. The heater would never work, running on cold oil wouldn't help the bearings and you'd need choke all day etc.
Don't think it would overheat without a thermostat like some cars, but have never tried it so can't be certain. That's where a temperature gauge would help.