As far as I'm aware I wouldn't worry too much about missing out the stress coat, I don't use it with my water changes and my axies seem to be fine! Is the stress coat a dechlorinator too, in which case if you wanted to change the water again to include the stress coat it should be fine to use without waiting another 24 hours.
Regarding the temperature of the water you are adding, unless it's below 16 degrees I don't think you need to worry as the axies like colder conditions. Though if you are doing 100% water change for some reason a sudden drop in temperature might stress them out. I use water direct from the tap/faucet (with dechlorinator) for partial water changes and just add it slowly, the axies seem to like it and come to have a look at what I'm doing, sitting near the incoming water flow!
I am a new axolotl owner, so if I'm wrong in anything I've said here I'm sure someone will correct me.
Kerry