The ODO entry for 'fervent' recommends to:
Compare with fervid and fervour.
I did read Etymonline's entry for 'fever' which doesn't explicitly answer this, but I think that I'd need to know rare linguistic variants to compare the etymologies and 'read between the lines' ?
Footnote: This article on the 'fiery' US TV series 'House of Cards' inspired this question.