Solved ABS bending on smaller prints

So I have a question regarding printed pieces with smaller surface area; when I try to print a small piece (say about the area of a quarter or smaller) with many layers, the piece warps. The problem is that the filament deposited on the previous layer is still pretty hot and when the extruder tries laying down another layer, the lower layers sort of bend around with it like jelly. I don't want to run a fan on the print and risk warping it even more, but how can I slow things down so that the layers have enough time to cool? I've even tried turning print speed down to 20 mm/s with no success. Any tips would be appreciated!

 

Thanks so much, Mark! I'm new to the 3D printing community so a lot of the basics still elude me. No more issues now that I've extended the layer time!