  Quantum phase transitions typically result in a broadened critical or
crossover region at nonzero temperature. Josephson arrays are a model of this
phenomenon, exhibiting a superconductor-insulator transition at a critical wave
impedance, and a well-understood insulating phase. Yet high-impedance arrays
used in quantum computing and metrology apparently evade this transition,
displaying superconducting behavior deep into the nominally insulating regime.
The absence of critical behavior in such devices is not well understood. Here
we show that, unlike the typical quantum-critical broadening scenario, in
Josephson arrays temperature dramatically shifts the critical region. This
shift leads to a regime of superconductivity at high temperature, arising from
the melted zero-temperature insulator. Our results quantitatively explain the
low-temperature onset of superconductivity in nominally insulating regimes, and
the transition to the strongly insulating phase. We further present, to our
knowledge, the first understanding of the onset of anomalous-metallic
resistance saturation. This work demonstrates a non-trivial interplay between
thermal effects and quantum criticality. A practical consequence is that,
counterintuitively, the coherence of high-impedance quantum circuits is
expected to be stabilized by thermal fluctuations.
