Is the use of the word 'damn' to express frustration offensive?

For example, will a sentence like 'It's so damn hot' be considered offensive by the person whom it is being said to?

It may be stereotyping, but mainstream US family (e.g. television) audiences, in particular, seem to prefer euphemisms for common low-level "cursing" - so darned, heck, gosh, dang and all the way to freaking as a not-so-mild option. These remove some of the potential for offence in mainstream use, particularly where children might be present, and then almost become habitual for some people. That means that it really does depend on your medium and your audience, as both the shock value of the language in Kick Ass and the rise of comics and recent film of Deadpool show that such timidity is by no means universal.

I've also found that many people are far more comfortable with 'language' than the stereotype would suggest, but it's not recommended to start a conversation by swearing as a way to test this early on. That's by no means a US-only statement: it applies equally to anyone, of any culture, pretty much anywhere: swearing as an opening gambit is at best ill-mannered, if not outright offensive.

In most other English-speaking places, the damn, Hell and similar at the low end wouldn't even be noticed in general speech, ranking very near to bloody, bollocks and bugger for harmlessness. Higher-end words still generate alternatives like naff off and feck, though, just in case your granny is listening.

My advice? If you don't know that's it's okay, don't say it.