Hopf bifurcation in thermal convection is an interesting phenomenon peculiar to the viscoelastic fluids. Employing a general constitutive relation which encompasses Maxwell model, Jeffreys model, Oldroyd-B model and Phan-Thien-Tanner model, the range of viscoelastic parameters where the Hopf bifurcation arises is determined when the viscoelastic fluid is confined in finite domains, which are compatible with the experimental situations. Employing the power series method, Landau equation is derived which determines the temporal evolution of the convection intensity in finite domains with nonslip sidewalls when the Hopf bifurcation occurs. The comparison of these results with the experimental data may be used to guide the selection of constitutive equations and to estimate viscoelastic parameter values.