The authors construct two approximate inertial manifolds for the following two-dimensional Newton-Boussinesq equations: \[ {\partial\over\partial t} \Delta\psi+J(\psi,\Delta\psi)=\Delta^2\psi-{R_a\over P_r} {\partial\theta\over\partial x},\quad {\partial\theta\over\partial t}+J(\psi,\theta)={1\over P_r} \Delta\theta, \] where \(J(u,v)=u_yv_x-u_xv_y\), \(P_r\) and \(R_a\) are the Prandtl and Rayleigh numbers respectively, and the flow function \(\psi\) and temperature \(\theta\) are required to satisfy given initial conditions and periodic boundary conditions. The orders of approximations of these manifolds to the global attractor are also derived.