You do not say what engine you have. If a 351 C you for sure need to have the correct thermostat to prevent overheating issues. I recently found a stash of the correct Stant one and sold the extras to forum members. The picture is of what you need for a 351- C. The HAT shaped part on the end of thermostat goes into the washer baffle in the block and changes the water flow when the engine is at operating temp. You should use the 192 deg. to get the best cooling.
With any engine you need a thermostat so that the water stays in the radiator long enough to get cooled down. With no thermostat the water circulates too fast and does not have time to cool. You might start out running cooler but like you say in traffic you will overheat.
The parts house will sell you a thermostat for the 351 that is not properly designed. The correct ones come up on Ebay but are expensive. There are kits to alter the system also but I have not tried them. The Stant # is S 333 192. You have to have the hat shaped end on the thermostat or it does not function correctly and does cause overheating issues.
We would even cut some of the impellers off the water pump on race engines to not only reduce the flow but get a little more HP. If you have a good radiator something else is causing your heating issues not just the gap in the shroud.
Rackerman is right about the top baffle not being on all cars. My original 73 mach 1 351 Q code 4 speed did not come with one. It has air and never had an overheating issue.
Your timing is also a big contributor to overheating.
When I install a new thermostat I drill a very small hole, 1/32" dia. in the flange to allow the air from the block to escape. This just keeps the system from burping when the thermostat does open up and insures there is not an airlock under the thermostat keeping it closed. The hole is small enough that it does not change cooling.
On the 302 engine you can put the head gaskets on backwards and cause issues also. You usually have water blow out after you have stopped and cut off the engine. You can verify if the gasket is right by pulling the core plug out of the front of the head and feel if the gasket is on correct.
I think the 351 can go on backwards also but no core plug to pull and check if correct.
Forgot to mention that if you have an automatic and are stopped in traffic put in neutral this reduces the amount of heat the transmission builds due to clutches slipping. You should put a cooler on the automatic to take the burden off your radiator also.
David