You can take the thermostat out of the car and remove the center. Don’t remove it completely or you may have the water blowing through to fast to cool. As for the core size, the bottom tank is what you have to go by in most cases. You can use the top tank on up to four runs most times, but the bottom is the width of the core, and a two run will be too narrow for anything wider. When you have any problems with overheating it is related to flow of air, or flow of water, if you’re using a good radiator. The reason today’s cars use smaller radiators and small electric fans is the heat transfer rate of aluminum is much higher than that of copper and brass. If you have a good Properly sized radiator you should be able to get enough air flow to keep your temperature wherever you want with The right thermostat, and the right fan setup IF as I read in many of the other posts, the water jackets are clean, and you used the right head gaskets.