In this research, a linear stability analysis for the onset of Marangoni convection in a horizontal layer of a nanofluid heated from below is investigated. The model employed forthe nanofluid incorporates the effects of Brownian motion and thermophoresis. The lowerboundary of the layer is assumed to be a rigid surface at fixed temperature, while the topboundary is assumed to be a non-deformable free surface cooled by convection to an exteriorregion at a fixed temperature. The boundaries of the layer are assumed to be impenetrable tonanoparticles with their distribution being determined from a conservation condition.The numerical computations are performed using the method of expansion of Chebyshevpolynomials. Stability boundaries for Marangoni numbers are obtained for several nanofluids. The new finding in this research is that the physical properties of the nanofluids arenot constants. These properties have been developed by several authors for various commonnanofluids based on an extensive survey of historical experimental data. It has been shownthat the solution to the steady-state problem represents a linear distribution in temperatureand an exponential distribution in volume fraction of nanoparticles. The assumption that thephysical properties of the nanofluids are not constant but functions of temperature and volume fraction of nanoparticle leads to new results of thermal stability that differ from previousresults.