My 1996 Ford F250 351 5.8L v8 has this issue where if it sits in the sun too long (an hour at least) then the truck will start and the battery level will show as low and the engine runs like crap for a while and then after about 10-15 minutes it will go back to normal battery level and the engine will run fine. This only happens when it is started when left out in the sun. when I keep it in the carport it does not happen. It has a brand new alternator. Not sure what to look for or how to fix the issue, any insight is appreciated.

 

How about if you tried leaving it out in the sun with the engine hood up/open ?
This is really a shot in the dark, but if it shows any kind of change we could be reasonably sure it is confined to the engine compartment. Far out, I agree, cheap test and no special effort involved. Some insight , huh? Let us know, this could help to isolate an area.