So are you saying you can overheat the engine without the tstat?

 

The cooling system is designed to be capable of dissipating at least as much heat as the engine develops.

The t'stat controls the speed at which the coolant flows through the system.
Coolant below the t'stat threshold means it doesn't flow until that threshold is met, whereby allowing the engine to reach operating temperature as soon as possible.
Beyond that, the hotter the coolant the more 'open' the t'stat and therefore the faster the coolant flows.

So whilst not having a t'stat means the coolant does not get to gain as much heat before moving on to the radiator, when it does get to the radiator, it doesn't have as much heat to loose before returning to the block, so the net effect is still a cooler engine until the system reaches it's operational temperature.
If the ambient air temp causes the coolant leaving the block is less than the threshold, the t'stat closes to slow the coolant flow and therefore raise the coolant/engine temp.

However, once the t'stat is open, the same condition exists as not having a t'stat.

Other than reaching operating temp sooner after startup, the t'stat does nothing in warmer climates.
In colder climates however, this is not true... without a t'stat, proper operating temp may never be reached.

The lack of a t'stat will not cause an overheat condition.