Most of the SM and SSM cars I've seen at Summit, mine included, run either no thermostat or a gutted stock one. I would suspect your lack of stat is not the problem. Miatae are particularly sensitive to missing pieces like the splash shield under the radiator, which contributes greatly to cooling. Also, make sure that the area between the core support and the bumper is blocked off to assure cooling air flows through the radiator and not around it.
Lastly, you said this is a new engine. (Lots of assumptions follow.) Depending upon what you had in place before, it is possible you are now making more horsepower and thus heat than you were before. It is possible to overwhelm the stock radiator even with a SM/SSM build. If any of this is the case, it is time to consider an aftermarket radiator. When my new motor went in last year (SSM build) it quickly caused my temp guage to read much hotter than it had previously, and that was with the ducting and shields in place and a good stock radiator. A decent aftermarket piece solved the problem for me.
YMMV.