There are at least three plasma instabilities associated with the electron heat flux in the solar wind. This letter reports the study of the unstable fast magnetosonic, Alfv¿n and whistler modes via a computer code which solves the full electromagnetic, linear, Vlasov dispersion relation. Linear theory demonstrates that both the magnetosonic and Alfv¿n instabilities are candidates for turbulent limitation of the heat flux in the solar wind at 1 A.U.