  We consider the initial boundary problem of 2D non-homogeneous incompressible
heat conducting Navier-Stokes equations with vacuum, where the viscosity and
heat conductivity depend on temperature in a power law of Chapman-Enskog. We
derive the global existence of strong solution to the initial-boundary value
problem, which is not trivial, especially for the nonisentropic system with
vacuum. Significantly, our existence result holds for the cases that the
viscosity and heat conductivity depend on $\theta$ with possibly different
power laws (i.e., $\mu=\theta^{\alpha}, \kappa=\theta^{\beta}$ with constants $
\alpha,\beta\geq0$) with smallness assumptions only on $\alpha$ and the measure
of initial vacuum domain. In particular, the initial data can be arbitrarily
large. Moreover, it is obtained that both velocity and temperature decay
exponentially as time tends to infinity.
