This 'harsh marker' thing is irrelevant for dissertations anyway because they are marked twice and any discrepancy is further moderated after discussions between the primary and secondary markers. Put simply, there isn't much opportunity to be marked 'harshly' in a dissertation because two people agree on the grade, then it is moderated another two times by the internal moderator and the external examiner.
If you have/had mitigating circumstances, you ought to follow the appropriate channels and procedures to apply them. Emailing the convenor isn't enough, is outside of procedure, and would be unlikely to result in anything at all.
Ideally, you'd have submitted mitigation before submission, as is the procedure at basically all institutions. However, if there are demonstrable reasons why you could do not do this, then the university might take into account retrospective mitigation. I must caution that this is very unusual, however.