I can not find the dimensions of the Core i3 stock cooler anywhere.
Will a Core i3 stock cooler fit in a 2U rackmount case?
I think it fits. The core i3 stock cooler is about 6-7cm tall and you have 88.1mm in a 2U case. Considering the motherboard is raised a little bit, the fan should fit marginally. But as mentioned by MarkM, you won't want to do that.