Your engine will run cooler than normal if you're running fluid through it full-tilt all the time. Probably not the worst thing for these bikes, particularly in the summer, but generally the recommendation is to run at the specified temps (and let the thermostat determine how to keep the engine block in that range). That said, it's easy enough to find second-hand thermo housing units here and on eBay for very little $$.
It should not hurt anything to run without a thermostat. It will take longer to warm up the engine on cooler mornings. As a resullt, fuel economy will drop until warm up, and emissions will be higher.
On colder days; around here I will ride until the temps are below 30 degrees in the mornings, the bike will probably not even register on the temp gauge unless you have a themostat in place in the system.
If I could find a replacement I would reinstall another one if mine were gone.
Just my opinion. As Said above, no harm done either way.
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