The reason why it may not be good to water many succulents and cacti when it stays hot at night - and by hot we are talking night time lows ~85F or higher is that most of the plants we are talking about have CAM respiration, which effectively means they breathe at night. However, at high temperatures they cannot reverse their circulation to breathe.
Having water around the roots is bad in that case for two reasons: it might still be taken up, without a way for the plant to actually deal with it, this can lead to quite sudden cellular deterioration and the plant turning to mush. In the slightly longer term the plants will be sitting in wet soil when in a state of what can be called dormancy just making it an inviting environment for rot to set in.
Every year here, when we start hitting summer, it is always interesting to see how the big box store garden departments deal with any succulent displays they may have sitting in their outside areas. Those that keep watering them as normal usually have trays of smelly black mush, whereas those that either stop watering them or bring them inside still have some decent looking succulents to sell.
It would appear that the night time low Ts above which these issues start to happen are not the same for all plants or at least depend in some part on the local conditions for the plant. It appears to be less of an issue with in the ground plants (soil probably stays cooler), but it is not unheard of for it to affect in the ground plants.
Here is a picture of an aloe, that suffered a sudden overnight deterioration. Wet soil unexpected few nights of >83-85F. The brown one was all gooey... I think the little ones may survive - they are sitting in my shade structure, I hope they make it through the summer.
