According to this entry from the The Princeton Dictionary of Buddhism by Buswell & Lopez, that monk is probably Sundarananda, often referred to as Nanda (not to be confused with Ananda):
After going to heaven, the Buddha takes Nanda on a journey to hell,
where he shows him the empty cauldron that awaits him after his
lifetime in heaven. After his enlightenment, Nanda came to the Buddha
to inform him of his achievement and to release the Buddha from his
promise of celestial maidens. It was because of his great will to
control his passions that Nanda was deemed foremost in self-control.
Unfortunately, the entry doesn't cite any source, only contains a brief mention of the poem Saundarananda by Aśvaghoṣa, where Sundarananda is the protagonist. I've skimmed through the poem - it dedicates one lengthy chapter to describe Nanda's journey to heaven, but nowhere does it depict him going to hell with the Buddha.
I found other mentions of him in chapter 5 of the Śūraṅgama Sutra, but only in the version with commentary by Master Hsuan Hua (宣化). Here is that piece:
After they finished touring the place the Buddha took his cousin down to the
hells. There they saw two ghosts heating a cauldron of oil. One of the
ghosts was sound asleep and although the other one was awake, he
didn’t have his eyes open. Nanda sized up the situation and thought to
himself, “These ghosts are suppose to be tending the fire under that
cauldron, but they’re not doing their job at all. Boy, are ghosts
lazy!” Then he meddled a bit and nudged one, saying, “What are you
doing this for?”
The little one’s droopy eyes popped open and glared at him. “What’s it
to you?” he snapped.
”I just wondered,” said Sundarananda.
”You gotta know, huh? Okay, I’ll tell you. The Buddha’s got a cousin
who’s cultivating the blessings of people and gods. He’s going to get
born in the heavens and enjoy 500 years of heavenly blessings before
he falls. Once he topples, however, he’ll come all the way down to
hell and when he gets here, we’re supposed to have this pot hot. He’s
to be deep-fried alive.”
Sundarananda was horrified and his hair stood on end. He suddenly
understood the whole picture and thought, “Those heavenly maidens are
ravishing, but 500 years of bliss with them isn’t worth it if I’m
eventually going to end up in a pot of boiling oil. I’d better follow
the Buddha, leave home, and be a monk.” So he forgot about Sundari and
One thing's for sure: this story is not a Jataka.