We demonstrate a new temperature record for image-current mediated sympathetic cooling of a single proton in a cryogenic Penning trap by laser-cooled ^{9}Be^{+}. An axial mode temperature of 170 mK is reached, which is a 15-fold improvement compared to the previous best value. Our cooling technique is applicable to any charged particle, so that the measurements presented here constitute a milestone toward the next generation of high-precision Penning-trap measurements with exotic particles.