I frequently wear a brange all day long, so to answer the questions.
No it does not get hot, even on the warmest summer days.
Wear a shirt or top that doesn't show the straps.
If you are getting strap marks on your body, then your bra is the wrong size, probably too small. My wife never has strap marks.
Sometimes a sports bra, but most often a full supporting bra, and finally
Yes you do get used to it, almost second nature and feel uncomfortable without.
