  Strongly disordered superconductors in a magnetic field display many
characteristic properties of type-II superconductivity--- except at low
temperatures where an anomalous linear $T$-dependence of the resistive critical
field $B_{c2}$ is routinely observed. This behavior violates the conventional
theory of superconductivity, and its origin remains a long-standing puzzle.
Here we report on systematic measurements of the critical magnetic field and
current on amorphous indium oxide films of various levels of disorder.
Surprisingly, our measurements show that the $B_{c2}$ anomaly near
zero-temperature is accompanied by a clear mean-field like scaling behavior of
the critical current. We demonstrate theoretically that these are consequences
of the vortex-glass ground state and its thermal fluctuations. This theory
further predicts the linear-$T$ anomaly to occur in films as well as bulk
superconductors with a slope that depends on the normal-state sheet
resistance---in agreement with experimental data. Thus, our combined
experimental and theoretical study reveals universal low-temperature behavior
of $B_{c2}$ in a large class of disordered superconductors.
