A common problem with older cars is that they either run too hot or too cold. Before trying to fix a problem that may not exist, you should first try to make sure that you are accurately measuring engine temperature. Cars would have either been equipped with a factory temperature gauge on the dashboard or an idiot light. It is easy to add an aftermarket gauge to supplement the warning lamp.
An engine's radiator is simply a water to air heat exchanger and it's job is to reject heat generated by the engine to the surrounding air. Heat transfer is a function of flows of air and coolant and the difference in temperature between the two. Increasing flow (air and/or coolant) and increasing the temperature difference both increase the rate at which heat is rejected from the engine.
Because an increasing temperature difference between air and coolant increases heat transfer, if an engine does not run overheat with a 160°F thermostat, it most certainly will not overheat with a 195°F thermostat. Engines tend to run more efficiently with hotter temperatures so it is better to use a winter thermostat year-round.
Often, a 160°F thermostat will be used to combat problems such as carburetor percolation or engine knock. For percolation, a better solution would be to use a better insulating gasket between the carburetor and intake manifold. For engine knock, a better solution would be to remove rust and scale from the engine's internals with a good cooling system flush.
NOTE: To avoid burns and injury, never, ever attempt to remove a radiator cap while the engine is hot!