Ah, yeah that's actually the worst thing you can possibly do really

. A japanese method involves brewing the coffee directly onto ice via pour-over, accounting for water content content when melted. The issue with letting it sit out to cool is it lets it oxidize and many coffees will become more acidic and bitter as a result. Cold brewing also removes a lot of the harsh taste from coffee, but it also doesn't really taste like real coffee to me so I prefer the Japanese method much more.
But yeah, pretty much anything will change flavor/experience depending on the temperature you have it, so no accounting for taste. Just letting you know you're kind of making it harder to really enjoy it by just drinking old coffee like that, the fresher the better, hot or cold.