A HSF is the most basic requirement. You can't run a computer without a motherboard, you're cpu won't survive without a heat sink and fan.
I would consider going for a cheap aftermarket cooler if you say your room is hot, or you have mid-high end equipment or your box doesn't have many ventilation points.
But if you don't overclock and don't want to spend money, stock will be tolerable.
An aftermarket cooler is a good consideration for any computer, extends your hardware's life and sound down.