Short Answer, Thoros does set Beric's sword on fire in the book as well.
Longer Answer: Thoros lost his faith in being a Red Priest when he could not convert Aerys II. He stuck around Westeros though and became friends with Robert. He would enter Melee's and use wildfire on his swords to scare his opponents horses. Three times he defeated Sandor Clegane this way. Gendry doesn't like Thoros at first because he destroyed many swords his master worked hard to build with his fire. He lost a Melee once simply because a common mace smashed his sword after the wildfire weakened it.
When Beric was killed by Gregor Clegane, Thoros began to get his faith back and breath life back into him, see things in the flames, etc. He was also able to create fire from blood and set Lord Beric's sword on fire without the aid of wildfire. However, the fire damaged the sword enough that Sandor was able to cleave it in two, as well as nearly cleaving Lord Beric in two as well.
Bonus fact: At the Tournament of the Hand for Eddard, Sandor Clegane won the joust. Thoros won the Melee. Anguy (the archer with Thoros) won the archery competition. Thoros also defeated Lord Beric in the joust. The money Sandor won in the tournament was stolen by the brotherhood, and it is what he wanted back from them.
Lately I've been really tempted to go through the entire show again and do write ups to provide extra information from the books to people who only watch the show in a non-spoiler way. I know a lot of people just watch the show, and while it is extremely loyal to the books, and when it isn't it goes back in a round about way that is usually easier for tv, a lot of the background information just cannot be there.
I think is a really cool idea!