In this paper, upper bounds of the decay rate for the Boussinesq equations are considered. Using the decay rate of solutions for the heat equation, and assuming that the solutions of the Boussinesq equations are smooth, we obtain the upper bounds of decay rate for the smooth solutions and difference between the solutions of the Boussinesq equations and those of the heat system with the same initial data. The decay results may then be obtained by passing to the limit of approximating sequences of solutions. The main tool is the Fourier splitting method. We consider the large time behavior of solutions to the Cauchy problem for the Boussinesq equations in n space dimensions. Here n is space dimensions, $u=u(x,t)$ is the velocity field of the flow, $ $ is the active scalar or temperature, $p(x,t)$ is the scalar pressure of the flow, $f(x,t) $ is the exteral potential. The Boussinesq equations are structurally similar to the Navier Stokes equations in fluid dynamics. Specifically, when the temperature $ $, the Bossinesq equations reduce to the incompressible Navier Stokes equations. Therefore, we solve the problem of the Bossinesq equations by referring to the study of the Navier Stokes equations. However, the Bossinesq equations contain the unknown function $ $, nonlinear terms and strong coupling terms, which make the study of Bossinesq equations more difficult. Moreover, gives rise to some new difficulties when considering the large time behavior of solutions. In this paper, we intend to study the decay of solutions for the Boussinesq equations, and the upper bounds of the difference between th solutions of the Boussinesq equatio andthose of the heat system with the same initial data. In Section 2, we give some properties and bounds for solutions of the heat equation.