  In this paper, we consider the two-dimensional (2D) incompressible Boussinesq
system with fractional Laplacian dissipation and thermal diffusion. Based on
the previous works and some new observations, we show that the condition
$1-\alpha <\beta<\min\Big\{3-3\alpha,\,\,\frac{\alpha}{2},\,\,
\frac{3\alpha^{2}+4\alpha-4}{8(1-\alpha)}\Big\}$ with
$0.7351\approx\frac{10-2\sqrt{10}}{5}<\alpha<1$ suffices in order for the
solution pair of velocity and temperature to remain smooth for all time.
