Running without a thermostat ok?
Yes. It is ok. But you need a restrictor ring. Same thing your thermostat provides when it's open. If you run a electric water pump you are not supposed to run a thermostat.
To the OP, keep in mind you will always run hotter than whatever T-stat you put in because it doesn't open until it hits that number. This doesn't mean it will run cooler without one or with a colder stat though. That will depend on the rest of your cooling systems capability.
