The word "distempered" means something that has no temperance, that is, it has no moderation and balance in its attitudes, in addition to making this exaggerated, unsettled and unwell. The excerpt, speaks of someone who is young but has a mind unprepared, uncontrolled and unwell.
Technachly, distempered means unevenly tempered, but in this excerpt, distempered has the same meaning as hotheaded, overheated, so overall, not tempered properly
so it could be healthy or unwell, depending on contex<span />