Effects of convective boundary conditions on the thermal instability of the conduction regime of natural flow in an inclined slender slot having very thin waits are investigated analytically for the type of instabilities occurring as longitudinal rolls, transverse rolls, and traveling waves. The Biot number H has a significant effect on the stability criterion when the instability sets in either as longitudinal rolls or as transverse waves in the form of traveling waves, but it has practically no effect on instability during the formation of stationary transverse rolls. When the transverse waves are dominant, the transition Prandtl number Prt, that is, the Prandtl number at which a changeover occurs from the stationary cells to the traveling waves, varies from a value of Prt= 12.7 when the vertical walls have prescribed temperatures to Prt= 0.95 when the walls have prescribed heat fluxes. The critical internal Grashof number decreases with decreasing Biot number. The transition angle, that is, the angle at which a changeover takes place from the longitudinal rolls to the transverse rolls, changes from δt= 72°(measured from the horizontal) with H →∞ to δt= 82°with H = 0 at both walls, for Pr = 0.72.