In the absence of gravitational effects, threshold values for the onset of convective thermocapillary instability are provided for a ’floating’ liquid layer open to the ambient air and subjected to internal heating along a divider located in a plane midway between two open boundaries. For steady modes of instability both the critical Marangoni number and the critical wavenumber are given as functions of the pervious and thermal properties of the heated divider. Also provided here are numerical estimates and velocity profiles amenable to experimental test under microgravity conditions.