Taking into account the effects of surrounding elastic medium and van der Waals forces between the inner and outer nanotubes and using the shell theory in continuum mechanics, the governing equation of carbon nanotube under the action of coupled thermo-mechanical load is established. Based on the model, an explicit formula for the critical load is derived in terms of the buckling modes of the shell and the parameters that indicate the effects of temperature change, surrounding elastic medium and the van der Waals force. Numerical simulation results show that at low and room temperature the critical load for infinitesimal buckling of a double-walled carbon nanotube increases as the value of temperature change increases, while at high temperature the critical load for infinitesimal buckling of a double-walled carbon nanotube decrease as the value of temperature change increases.