Surface deformation and capillary instability of nonisothermal liquid bridges have been analyzed. The results show that the maximum size of the bridge is limited by the capillary instability. When the length of the bridge increases, a nonstationary surface deformation may occur before the capillary instability sets in, and it may lead to an earlier breakup of the bridge. Detailed calculations have been carried out for cylindrical bridges. It has been found that such bridges bulge at the cold end and constrict at the hot end. An asymptotic form of surface deformation has been identified in the case of very short bridges.