Hydrodynamic stability of a two-dimensional steady thermocapillary flow under weightlessness in a high-Prandtl number liquid bridge is studied by means of three-dimensional numerical modeling for a wide range of aspect ratios. We suggest an explanation of the findings of a series of microgravity experiments on Marangoni convection in liquid bridges. Stability of the flow with heat transfer through the interface, modeled by the classical Fourier law, is compared with the stability of the same system under adiabatic conditions. Cooling the interface may significantly shift the threshold of hydrothermal instability as soon as the Biot number deviates from zero. It may also affect the structure of the basic Marangoni flow and the mode of the supercritical flow. We demonstrate that the heat loss has a destabilizing effect for the aspect ratios (ratio of radius to height) below 2.4 (with the exception of a region between 1.6 and 1.8), and for the longer liquid bridges the prevailing effect is stabilizing. The heat transfer coefficient as a function of the length of the liquid zone is theoretically calculated using a model of heat transport for laminar forced convection. Comparison of the results of the modeling with the experimental data shows that an incorrect assessment of the heat transfer may lead to wrong conclusions concerning both the critical parameters of the flow and its structure. (C) 2015 Elsevier Ltd. All rights reserved.