I live near the southern California desert where temperatures change quickly. Now it is in the mid 40s during the night, but can be in the 80s during the day. My Brazilian Rain Tree is in its nursery container - it gets watered daily. Some leaves are turning yellow, yet there are new branches growing with new leaves. Many leaves are folded during the day whether in shade or sun.

Should I bring it in during the night?

This is not a species I have any direct experience of but it seems likely that the temperature variation you mention may be just too much for the tree to cope with happily and it is showing signs of stress as a result. Or, has it been repotted recently as this can also stress the tree. Might well be worth bringing indoors if the forecast is less than 55 or so at night

Dave