We perform a theoretical analysis of the onset of convection in a layer of near-critical 3He submitted to an unsteady bottom heating. A theoretical model previously presented [P. Carlès, Physica D 147, 36 (2000)] is adapted to the corresponding physical conditions, and a method is proposed to solve the associated equations. We predict, for different intensities of heating and different initial temperatures, when convection will start and what will be the shape of the dominant growing perturbations. A systematic parametric analysis shows that the onset of convection in a supercritical fluid can take place following four distinct scenarios, depending on the initial temperature and the intensity of the heating. Two of these scenarios are entirely specific to near-critical fluids, being impossible to observe in classical Boussinesq fluids.