Anything that's perfervid is full of an intense, deep emotion. Your perfervid speeches begging your parents to get a dog may do no good if they're both allergic.
When feelings are impassioned and intense, they're perfervid. The word's Latin root, fervidus, means "glowing or burning," and it also gave rise to the adjective fervid, "intensely enthusiastic or passionate." Perfervid doubles down on that emotion by adding the prefix per-, "utterly or completely." So use it when your feelings are at their most intense: "The perfervid protesters demanded to be heard."