Brute force won't work, but any other effect will work, provided it is hit point-dependent

At first blush, the 20th level Zealot Barbarian seems unkillable, and this is true if you play the Barbarian's game by engaging them in direct melee combat. Indeed, by RAW the Barbarian could massacre an entire army of mundane soldiers and continuously maintain their rage until they were able to find any sort of healing to recover the minimum 1 hit point necessary for them to keep on trucking.

However, 5e has a handful magical effects that can be used to reliably handle this situation, though.

• Sleep: It's only a 1st level spell, but if you can reduce the Zealot's hit points enough (or upcast the spell high enough), you can forcibly end the rage by knocking them unconscious. If you do this when the Zealot is at 0 hit points and has failed 3 death saves, they will die on the spot.
• Power word kill: If you can get the Zealot below 100 hit points, you have the option to drop them outright with this.

This is a fairly short list that curiously hits both ends of the spellcasting spectrum, but either will stop the Zealot on the spot.

There are a few other options accessed by turning into a creature with true polymorph or some other method to access them. These all require you to reduce the Zealot to 0 hit points, be aware that it can be difficult to do this because the Zealot can make several saves due to Relentless Rage to instead be reduced to just 1 hit point:

• Shadow Dragon's Shadow Breath (MM, p. 85) will instantly kill a creature reduced to 0 hit points by this attack.
• Mind Flayer's Extract Brain (MM, p. 222) will instantly kill a creature reduced to 0 hit points by this attack.
• Phase Spider's bite attack will paralyze a creature for 1 hour if the poison reduces them to 0 hit points, which means that the rage will lapse after 1 minute and the Zealot will die.
• Swarm of Centipedes' bite attack (MM, p. 338) will paralyze a creature for 1 hour if the poison reduces them to 0 hit points, which means that the rage will lapse after 1 minute and the Zealot will die.

These methods are most viable after you've reduced the Zealot to 0 hit points since you won't trigger their Relentless Rage, which the Zealot can probably reliably make 2-3 times before it starts getting tricky. I've avoided effects that rely on trying to reduce the Zealot's maximum hit points to 0. While they technically would work, you would find yourself spending an absurd number of rounds trying to reduce a feasible 275 maximum hit points.

One last method that would reliably work is:

• Forcecage: Trapping the Zealot in creates a situation whereby you can plink down the Barbarian's hit points and implement any of the other strategies.

As mentioned in the answers to the linked question, the rules for temporary hit points state:

Unless a feature that grants you temporary hit points has a duration, they last until they’re depleted or you finish a long rest.

Since no duration is mentioned here you assume they last unless they are replaced by another spell, used up or the target takes a long rest.

This is all valid by RAW and you should not worry about it being too OP. It has been out for over a year now and no errata has been published. Just have fun with it.