1982 Chevy El Camino Engine Overheated

I drove the above subject 45 miles not realizing it was overheating since the light never came on. After letting it cool off, I tried to re start and the starter just click and would not turn the engine. Thought starter had gone bad I changed the starter and made sure the battery was fully charged. Tried again and the engine will not turn. Very strange when it was running fine. Could the engine have locked up from getting to hot? Thanks