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Q:

drive train on 1993 Ford E-150

Rookie cbe0621eac06868b3efe0d8d1d3611e23c60d3114864ea2ec19a68cfbd3eebab
drive train would not go in to reverse when engine is hot
(1) Answer
Are you sure this is a 1993 with a 5.0L V8? I'm not showing this combination in 1993.

If it is indeed a 5.0, you probably have a fully mechanical AOD transmission. This is vacuum operated. I would look for a possible vacuum supply issue. You could have an internal mechanical concern too.