Wouldn't it be a bit worrisome if the hand was warm enough to feel it through the gloves, or am I just stupid?
Depends on the quality, the time spend wearing the gloves and purpose of the gloves.
Seeing as the admiral depicted in Kancolle is generally working with paperwork inside a building my guess is that the gloves are relatively thin and breathe aplenty. Their purpose mainly to prevent too much smearing when working on the paperwork.
I hope this might at least give some ideas how the heat would transfer relatively easily?
Gloves intended for indoor work are generally thinner (unless it is construction and industrial work).