It sounds like this is Cherry Bomb or if not, then a similar cultivar of C.Annuum with a rounded cherry/tomato shaped fruit (about an inch in size) and a fair heat - roughly comparable to a jalapeno? (hotter than an anaheim but sweeter than a serrano or habanero).
'Sweet' cherry peppers are also available without any of the heat.
As such I think it will survive the heat as well as any other C.Annuum (ie. most pepper cultivars - bell peppers, jalapenos, etc).
This summer we've had sustained highs in the 40-45 range for a few months, and my peppers have survived fine. I water them every other evening. Most of them are in beds, but a few (pepperocinis and ornamentals) are in pots. Give them a lot of water. For your higher temperatures, I would probably water them every evening. A mulch to keep the water in is probably worth investigating.
The leaves will go limp due to drought stress - this is a natural response. Limp like polythene, but should perk up with good watering. In more extreme cases, when they perk up they'll have some dead curling of the leaf edges (I've noticed this on a couple of mine but they are at the edge of a raised bed - so it probably drains/dries more quickly).
Note for your pottery pot: It might cool quicker, but if it is in the sun, it will still heat up quickly - you may need some shade.
If direct sun is a problem, you may also need to shade any fruit - especially if the plants have only moderate foliage. Pepper fruit will scorch in strong direct sunlight.
They say heat is required for decent 'hot' peppers. I've managed to make some good chilli powder from Cherry Bomb (just be careful to wear gloves when cutting them - the capsaicin managed to heat-sensitise my hands for a few days afterwards!)