‘Heated Rivalry’ Cried Out for Satire. Edinburgh Fringe Heard the Call.

If ever a television show was crying out to be lampooned, it was “Heated Rivalry.” The Canadian series, which depicts a secret gay romance between two elite ice hockey players on opposing teams, became a hit almost in spite of itself. The show’s story line is the stuff of fan fiction, the characterization is paper-thin, and even the sex scenes feel strangely sanitized. But viewers find its guileless sincerity compelling — and this makes it ripe for satire.

It is still something of a surprise, however, that there are not one, but three ultra-campy musical tributes to “Heated Rivalry” at this year’s Edinburgh Festival Fringe, which runs through Aug. 31. One of the shows is an offshoot of the Off Broadway production that has been drawing audiences in New York since spring and was recently extended through November; the others are new.

The funniest is “Heated Rivalry: The Musical Parody!,” written by Andrew Young and Molly Moseley, and featuring Jamie Ary as the talented-but-drippy Canadian hockey whiz Shane Hollander and Rob Warner as his laconic Russian nemesis-turned-lover, Ilya Rozanov. Their opposed personality types are grotesquely exaggerated for comic effect: Shane is so dull that he folds up his shorts before lovemaking, and Ilya is sullen to the point of rudeness.

The show is delightfully scrappy. During a gym scene, two black-clad ensemble performers get down on their knees and put their hands in shoes to simulate the Peloton machines that Shane and Ilya train on. Blue tinsel stands in for streams of water during the shower scene in which Ilya makes his first advances on Shane. As in the series, we get a cover version of Tatu’s “All the Things She Said” — except here the words of the chorus are altered, for legal reasons, to “Couldn’t get the rights.”

The actors, accompanied onstage by a keyboardist and a guitarist, cavort suggestively with hockey sticks, and there is much fun with double entendres. A sports commentator zestily calls out “Ooh, bodycheck!” Shane’s mother, oblivious of his sexuality and desperate for him to outshine Ilya, urges her son to “Bring him to his knees!” Ahem.

This ribaldry is combined with an affectionate but incisive skewering of the TV show’s clunky shortcomings. Ilya’s surly father signs off an early rant with “See you in episode five, when I die.” Shane and Ilya’s doomed female love interests, Rose and Svetlana, magnanimously accepting of their fate, sing a self-congratulatory number about being great allies to L.G.B.T.Q. people. And Scott Hunter, a fellow hockey pro whose on-air coming-out inspires Ilya and Shane, leads a happy-clappy anthem about the utopian future awaiting us at the end of the series’ timeline — “When Everyone Is Gay in 2019.”

What if it’s not really that deep, and the TV show’s touchy-feely messaging was just a convenient pretext to peddle soft porn to the masses? This is the suggestion mischievously posited at the outset the Off Broadway show, which is playing in Edinburgh with a new cast. “Heated Rivalry: The Unauthorized Musical Parody” (don’t be misled — none of these shows are “authorized”) is MC’d by an American homemaker called Susan (May Tether) who, it is implied, represents a big chunk of the TV show’s target audience. In a stomping opening number, she tells us that her only desire is to watch “gay hockey players with big butts having sex.”

Butts are a recurring theme. In this retelling, directed by Alan Kliffer with a book by Dylan MarcAurele, Ilya (Joseph Dann, in his stage debut) nurses childhood trauma over his “supersize caboose,” as well as mummy and daddy issues. Zheng Xi Yong’s Shane listens to classic Broadway tunes while exercising on his Peloton, and whines like a stroppy schoolkid whenever things get tough. The dynamic between them is more or less parent-child.

The vocal performances here are stronger and more earnest, which makes the incongruity with the lyrics — ranging from the merely filthy to the unprintable — all the more amusing. There are more double entendres and some lovely moments of comic bathos: Ilya believes his mother’s killed herself years earlier out of shame over his sexuality, only to eventually realize that he hadn’t read her suicide note to the end — and she was, in fact, OK with it.

The vibe is very different in “Puck Bunnies: A Heated Rivalry Drag Musical Parody,” where the pianist and musical director Tony Gonzalez is the only male-identifying performer in the company. As he plays the keyboard in one corner of the stage, the drag kings Hanna Barlow and Kyra Brown, playing Shane and Ilya, prance around in glittery hockey jerseys, which they lift to reveal chiseled male torsos made of silicone.

The title “Puck Bunnies” — a slang term for women who follow men’s ice hockey mostly because they’re into the athletes — is knowingly ironic for a show that celebrates queer joy. It isn’t quite as witty as the other two shows, and once the initial novelty of the gender switch wears off, the comic energy starts to dissipate. But it’s never dull.

The repartee is crowd-pleasingly crass, such as when Scott’s barista boyfriend, Kip, offers to add “nine inches of extra girth” to Scott’s smoothie. (It’s a banana, of course.) At one point, a sex act is rendered using outsized inflatable genitalia.

What all three musicals have in common, subject matter aside, is a relentlessness exuberance that exemplifies all that’s best about theater at the Fringe. And they point to something significant about the nature of casual fandom in the era of viral media — not real, obsessive devotion but its water-cooler counterpart, which has ambivalent curiosity at its core.

When a show becomes a meme, the meme becomes the story, eclipsing the show itself. This phenomenon is here to stay. Thankfully, we’ll always have satire.