180 or 190 thermostat?

Dead wrong.
190* opens later & closes sooner= hotter heat. Not exactly what you want in summer driving sitting in traffic. Even a 190* t-stat won't give you heat any quicker, just more consistant hotter heat on cold days.

As other have posted the thermostat temp rating has little effect on maximum(peak running) temperature. However running the engine without one can cause higher temps because the water flows through the engine too quickly & doesn't allow for the necessary heat transfer from the engine into the water.

180* t-stat should be fine.
The "too fast thru the engine" theory is frequently debated on forums all over with no resolution. I contend that's not the problem at all. Water is an excellent coolant, it both easily picks up heat and dumps it. Hard for me to believe it can be flowed thru the contortions that make up a coolant jacket too fast for it to accept only a very small amount of heat.

What does happen is that without a t-stat there is no restriction to flow at the outlet, so the coolant pressure in the block is lower and only due to those same contortions. With a t-stat block pressure is higher than cap pressure by some significant margin. With a lower block pressure it is easier to boil the coolant in localized hot spots. Once boiled it doesn't accept heat so readily and it takes a lot more effort to cool it back down.

Those disc type restrictors sold to replace a t-stat are OK for drag racing, but for any kind of road course, off road, or endurance racing they're junk. The restrictor for that type of use needs to be a venturi type of shape. Probably would need to be inserted in the hose *just* beyond the t-stat housing rather than in the t-stat's location to work best.

FWIW I ran a 195° t-stat in my old '67 Ranchero with a mild 302/AOD combo that saw a lot of desert towing miles. Ran it year-round with a Stewart Components pump and a cross-flow radiator. With an old 4 cyl hot rod that I had years ago I could tell by the power what the temp was. At 160° it made the most power, but at 180° it got the best mileage by a substantial amount. I ran a 180° in it. Didn't need the difference in power all that often, but being a poor working kid I needed the mileage.