The fridge option is usually best for a sick/ailing axolotl especially during summer temperatures where you can't get the tank down below 22C and maintain it.
Axolotls are cold water creatures - they do not adapt/acclimitise to warm temperatures despite what some people might think .
Anything below 20C is usually ideal - down to as low as 5C.
Hence when an axolotl is sick, placing it in the fridge slows its metabolism down to give it a chance to heal.
Keeping an axie in warm/summer temps 22+ when it's sick just makes things worse - an axies immune system basically can become lowered/compromised and therefore they (or usually the weakest axie of the bunch) will start showing symptoms of odd floating, deteriorating gills/limbs, odd out of the normal behaviour, skinnieness and/or fungal infections. This can take anywhere from a few days to several weeks to develop depending on water conditions, companions they're kept with (or if unquarantined companions have been added to tank) or heat. Predominantly, especially in Aussie at the moment the majority of stress or illnesses have been related to extreme temperatures.
Many axolotl owners (a few in Australia, parts of Europe/UK and USA) place their axolotls in the fridge for the summer months until it cools down enough for them to come out again (below 18C).