Some English usage authorities draw a distinction between fervent and fervid, saying that while both mean having great passion or zeal, fervid feelings are more extreme and perhaps irrational than fervent feelings. In other words, fervidness is ferventness to an excessive degree. While this distinction might be useful, it is not consistently borne out in real-world usage. The word are generally interchangeable, with fervent being the more common form by a large margin.
Trying to make these words anything but variants of each other would be practically impossible because they sound so similar and are both rare, and because the supposed different between them is so subtle. Similar-sounding words that are not rare and whose meanings differ in not-so-subtle ways can stay separate because people hear and use them often enough to feel comfortable with them. That is not the case with fervent and fervid. They will stay synonyms until they become much more common than they are.
It would be possible to cherry-pick a few examples showing that fervent and fervid sometimes mean slightly different things, but for the most part there is no obvious difference between them. We have chosen these examples more or less at random:
Gen MacArthur was a fervent anti-communist, so his argument made a strong impression on Kennedy. [Financial Times]
The Avro Arrow attracts a special breed of fan — one devoted to the legend, who soaks up the mythology and history with a fervid passion. [Toronto Star]
By no means were all of these men and women fervent Nazis, anti- Semites or bigots. [Modern German Literature, Michael Minden]
That left the small but fervid legion of believers who had dropped everything feeling upset and sheepish. [Daily Beast]
As a fervent anti-recliner, it’s embarrassing and an annoyance to have to spend the whole flight pulling the seat upright. [Sydney Morning Herald]
The stadium infield was filled with the Colorado Party’s most fervid supporters getting more fervid all the time on sugarcane rum. [Give War a Chance, P.J. O'Rourke]