the huge amount of surface area would nonetheless heat up and be visible in the infrared
Unless you're spending some of the energy the Dyson sphere is collecting to actively cool that surface area.
all the energy would eventually get absorbed/used SOMEWHERE
Sure, but if you point it at another galaxy, it will take a very very long time for something to happen (and in a galaxy far, far away, too).
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.
To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.