IMHO, not knowing what tolerances the internals are, I would say a stat would definately not "hurt anything". I would say a 160*F stat and keep the flow good would be great.
The biggest problem with headers is the lack of the ability to "preheat" the water, this cause issues with even temps across the entire block/heads...
Now if it was mine, I would do a rear water outlet setup, or have the entering water go in through the drain holes in the block.. It works good both ways..
GT