I was reading this answer and I came across this:
(A) 何もしないで暖かくする (ambiguous)
(B) 何もしなくて暖かくする (unambiguous)
I'm not sure why A is ambiguous, but here's my understanding: unlike なくて, ないで doesn't imply a cause, so it could either mean that not doing anything keeps you warm or not. However, in the same answer, it says that B does not mean "keep the body warm by not doing any activity," which contradicts what I know about なくて, that is, it implies a cause. In other words, I would translate both as follows:
Somebody doesn't do anything and keeps warm.
not necessarily Somebody keeps warm by not doing anything.
Somebody keeps warm by not doing anything.
not Somebody doesn't do anything and keeps warm.