  We revisit the 2D Cauchy problem of nonhomogeneous heat conducting
magnetohydrodynamic (MHD) equations in $\mathbb{R}^2$. For the initial density
allowing vacuum at infinity, we derive the global existence and uniqueness of
strong solutions provided that the initial density and the initial magnetic
decay not too slowly at infinity. In particular, the initial data can be
arbitrarily large. This improves our previous work where the initial density
has non-vacuum states at infinity. The result could also be viewed as an
extension of the study in L{\"u}-Xu-Zhong for the inhomogeneous case to the
full inhomogeneous situation. The method is based on delicate spatial weighted
estimates and the structural characteristic of the system under consideration.
As a byproduct, we get the global existence of strong solutions to the 2D
Cauchy problem for nonhomogeneous heat conducting Navier-Stokes equations with
vacuum at infinity.
