In this paper we consider a thermal multiphase lattice Boltzmann method (LBM) to investigate the heating and vaporization of a suspended droplet. An important benefit from the LBM is that phase separation is generated spontaneously and jump conditions for heat and mass transfer are not imposed. We use double distribution functions in order to solve for momentum and energy equations. The force is incorporated via the exact difference method (EDM) scheme where different equations of state (EOS) are used, including the Peng-Robinson EOS. The equilibrium and boundary conditions are carefully studied. Results are presented for a hexane droplet set to evaporate in a superheated gas, for static condition and under gravitational effects. For the static droplet, the numerical simulations show that capillary pressure and the cooling effect at the interface play a major role. When the droplet is convected due to the gravitational field, the relative motion between the droplet and surrounding gas enhances the heat transfer. Evolution of density and temperature fields are illustrated in details.