How cold is too cold?

[Lefitte]

After spending my first full summer with a snake for a pet (and with a more sensitive species on the way), I've been a little worried about the way my house doesn't always cool down at night. After my kingsnake Eir seemed a little restless after a few days of 83 degrees, I decided to sort of make up my own "cool hide" but I'm a little worried about safety.

1. How cold is too cold for temporary, voluntary conditions?
2. What are some of the negative outcomes? Is frostbite or something like that a concern here?
3. Will the snake move before getting too cold or is there a chance of getting too cold and being unable to move away to find heat?

Snakes: Year old California king, baby BRB

Here's what I've got:
I'm taking an insulated lunch bag and putting a small ice pack wrapped in a paper towel at the bottom, folding the bottom up and using it like that. The snakes still have access to the ice pack directly if they want to. I'm currently testing the temps and the middle of the bag was staying in the mid-60s while directly on top of the ice pack was 58-60F. This idea provides my snakes with a chance to cool off during the day when my house and climate refuse to see 79. We cant really afford to run the air any more than that during summer. I live in a desert that can get 115+ during the day and mid-80s for nighttime lows in the height of summer so trying to get my house below 80 just isn't feasible and neither is a small a/c unit. Fans with ice in front of them become bowls with water in thd blink of an eye so this seems like a better option. I just want to make sure that it is safe and wont do any harm to them.

If this idea works, I want to cut up some lunch bags and stick them to a plastic hide so that it looks a little better and works the same way, I could get some netting or some to block direct contact with the icepack with this idea as well and it wouldnt look so ugly as a lunch bag sitting in a snake cage.