I imagine you will get a different definition of idle depending on who you ask......for me....if the computer boots to windows.....and then sits....that would be idle.
Also, even if you have 5 tabs open, but the CPU isn't actually doing anything with the tabs.....that would also be idle in my opinion.
Pretty much anything with a real low CPU usage.....like under 10% I would call idle.
....and like you....I don't know why the temps went up with the new case....but I would still consider a new cooler.....there is a big difference between the louder coolers and the quieter ones....around 15 decibels.....that's quite a bit.
https://www.anandtech.com/bench/CPUCooling/774