Dust can be a major cause, especially if it is an older PC that has not been cleaned and the temperatures have gradually increased from better temperatures.
If this is a new PC, then dust is not a factor and installation of the heatsink/fan is the issue.
Even a stock cooler should not let a PC heat up that much on idle, so the only way the new cooler will resolve the issue is because you will be -re-doing the cooler installation and you might get it right this time.
Of course, if you live somewhere where ambient (room) temperatures are 45C or more, or if you work alongside a furnace, or if your name is Lucifer and part of your address includes the word "Hades", then please disregard all of the above.