The heat transfer between hot fluid and cup surface occurs thru the cup wall thickness. Thicker the cup wall slower the heat transfer rate.
Transfer to cup handle occurs along length along the handle. So portions of handle close to cup handle intersection hotter than portions away. The area of x section thru which heat flows is simply cross section area of handle. Which is quite small. So heat transfer rate much smaller.
As philosophyyyy stated in a laconic manner.
