Meaning：
＊a very strong form of “please”, but we often use it almost as an expletive or something we say when we are angry.
Synonyms:
‘for God’s sake’ or ‘for Christ’s sake’

Other similar idioms are “for the love of God” or ‘for crying out loud’ but these are more used for emphasis without any particular meaning.

Sentences：

For heaven’s sake don’t do that again! Or I shall get very angry.
For heaven’s sake, stop talking about Terry!
For heaven’s sake, why didn’t you call?

Conversation 1

A: Will you turn the TV down please? I’m trying to study.
B: Yeah just a minute, I’m just watching this.
A: Oh, for heaven’s sake will you turn it down now!
B: Ok,Ok, calm down, don’t get so worked up about it.
A: All I want is some peace and quiet.

Conversation 2
A: Have you seen my book anywhere? I’ve been looking for it everywhere.
B: Umm, I’m not sure, what does it look like?
A: You know, the dark blue one.
B: Oh yeah, I think I’ve seen it somewhere.
A: I’m going to be late if I don’t find it. For heaven’s sake, where is it?
B: Oh here it is, I was sitting on it!! Sorry!

Conversation3
A: Will you do the washing up please? It’s your turn.
B: Oh, can I do it in a minute, I’m just in the middle of something.
A: Well I want to cook something and everything’s dirty.
B: Yeah, I know, but I’m busy now!
A: Oh, for heavens sake! I’ll do it myself.

(Callan book5, Stage 9 826p)