  We investigate the upper critical field in a dirty two-band superconductor
within quasiclassical Usadel equations. The regime of very high anisotropy in
the quasi-2D band, relevant for MgB$_{2}$, is considered. We show that strong
disparities in pairing interactions and diffusion constant anisotropies for two
bands influence the in-plane $H_{c2}$ in a different way at high and low
temperatures. This causes temperature-dependent $H_{c2}$ anisotropy, in
accordance with recent experimental data in MgB$_{2}$. The three-dimensional
band most strongly influences the in-plane $H_{c2}$ near $T_{c}$, in the
Ginzburg-Landau (GL) region. However, due to a very large difference between
the c-axis coherence lengths in the two bands, the GL theory is applicable only
in an extremely narrow temperature range near $T_c$. The angular dependence of
$H_{c2}$ deviates from a simple effective-mass law even near $T_c$.
