There is another sense of 'minded (which has nothing to do with caring about something), but it is rarely used now: you could say 'He is minded to do it'. But note that this is invariable; you can't inflect the fossilized verb. This sort of 'minded' is typically used by judges before their summing up: 'I am minded to acquit but will review the testimony before I pass sentence.'
You could also 'He has it in mind to do it' (meaning he's thinking of doing it).
b