If it says that it is a Tray processor, then no, it doesn't come with a heatsink-fan unit. But, i it doesn't mention 'Tray' and it doesn't specifically say that no heatsink-fan unit is included (this is the case with some eXtreme processors), then yes, it should contain a heatsink-fan unit.
This listing, https://www.amazon.com/Intel-i3-10320-Desktop-Processor-LGA1200/dp/B086M4KSMW, says that it does include the heatsink-fan unit (a.k.a. Cooler).
This listing, https://store.immediasys.com/core-i3-10320-8m-cache-up-to-4-6ghz-fc-lga14c-tray-cm8070104291009, on the other hand, is a tray processor and comes without the heatsink-fan unit. NOTE: Tray processors do not have a warranty! Do not purchase one. They are not meant to be sold to the public.