Aquarium Silicone, perhaps?

I have a 50 gallon barrel that is the basis for a water garden home made filter system. It developed a 3" crack near the top. I used a 1/8" drill bit and did "stop drilling" at each end of the crack and coated it inside and out with "Flex Paste". I allowed the water level so stay below the crack for 24 hours so the paste could cure and has performed well for 3-4 months now.

I'd avoid doing the melting/welding in the crack It would be too rigid and with any movement the crack would appear again. You need something with some flexability. The aquarium silicone should work well with some sort of flexible/ rubber-type of patch, on the inside of course. And drilling "stop holes" either end of the original crack as suggested will help stop the crack from extending. Any movement or flexing of the tank would be mitigated by the patch. Weight of the water in the tank will keep the patch firmly pressed against the crack. Hard to go wrong.

There are waterbed patch kits avaivable for fixing leaks in vynil mattresses. not sure about capacity, but king mattress takes a lot. and free flow moves a lot, so it will withstand a lot of pressure. but outside it has exposure to sun too , but the glue might be strong enough.

also search for pool patch kits , like above ground plastic pools.

like here:

https://backyardsidekick.com/how-to-patch-an-inflatable-pool-fix-it-and-repair-guide/

Thanks everyone! I won't be able to do this until Fall, since I have a huge waterlily growing in it. The crack is small and the leakage is minimal so far. I'll keep my eye on it and if it gets worse, I guess I'll have to figure out what to do with this huge waterlily (and the million tadpoles that live in the tank). If I can wait until later Fall, after the stocktank is drained, would it be better to do it early next spring, so it doesn't live through winter first? I wonder what causes these cracks.....might it be manipulating this big stocktank to turn it over in winter and then back up again in spring........or could it be a slight unevenness when it's full? I'm sure the sun is hard on it too. I have 2 in-ground 300 gallon stocktanks and (knock on wood), they've been leak-free for at least 15 years. But that's probably because of never being moved or exposed to the sun. I'm going to print off all your suggestions so I have easy access to them when the time comes. I really appreciate everyone's suggestions!

You could just duct tape it until then , several layers. it will reduce seepage. i think there are sprays that protect from UV/UVA damage.. for various materials. plastic becomes brittle with time from hot/low temp exposures.

Would duct tape stick to a wet area? We have lots of duct tape here. hahaha

if it's ye old gray plumbing duck tape not designer colors.. :O ,, it sticks to wet.. ;)))

Thanks petrushka, I'll give that a try. I'm not a designer-type person and have probably too much old gray duck tape around......so I'm good. :) It's our "go-to" fixer upper. hahaha