  The body-centered-tetragonal antiferromagnet EuGa$_4$ exhibits A-type
antiferromagnetic order below its N\'eel temperature $T_{\rm N} = 16.4$ K in
magnetic field $H = 0$ where the moments are ferromagnetically aligned in the
$ab$-plane with the Eu moments in adjacent Eu planes aligned
antiferromagnetically. Previous magnetization versus field $M_{ab}(H)$
measurements revealed that the moments exhibit a spin-reorientation transition
at a critical field $H_{c1}$ where the Eu moments become perpendicular to an
in-plane magnetic field while still remaining in the $ab$ plane. A theory for
$T=0$ K was previously presented that successfully explained the observed
low-field moment-reorientation behavior at $T = 2$ K. Here we present a theory
explaining the observed $T$ dependence of $M_{ab}(H,T<T_{\rm N})$ in the
[1,0,0] direction for $H\leq H_{\rm c1}(T)$ from 2 to 14 K arising from a
$T$-dependent anisotropy energy.
