Multiple tenses are not a problem, and are often required in complex sentences handling events at different times.
However, the tenses and voices in the original sentence and your suggested alternatives are not correct.
There are two equally good ways to fix the original sentence - depending on whether you really want to place events in the past or not.
You should not work in the field while the sun is hot.
(Present conditional "should [not] work" plus present active 'is').
You should not have worked in the field while the sun was hot.
(Present perfect conditional "should [not] have worked" plus simple past 'was').
I've created these two alternatives as your attempts to fix the sentence seem to be aiming for the present tense and perfect tense respectively.
The main problem with the original sentence and your suggestions if the use of the present progressive, which is not needed or appropriate in the context.
The present continuous conveys the meaning of something happening right now and continues to happen. You can technically say "the sun is being hot" or "the sun was being hot", and it is grammatically fine and logically true. All I can say is that it is not idiomatic ... it sounds really weird.