  We theoretically investigate the temperature-to-phase conversion (TPC)
process occurring in dc superconducting quantum interferometers based on
superconductor--normal metal--superconductor (SNS) mesoscopic Josephson
junctions. In particular, we predict the temperature-driven rearrangement of
the phase gradients in the interferometer under the fixed constraints of
fluxoid quantization and supercurrent conservation. This allows sizeable phase
variations across the junctions for suitable structure parameters and
temperatures. We show that the TPC can be a basis for sensitive single-photon
sensors or bolometers. We propose a radiation detector realizable with
conventional materials and state-of-the-art nanofabrication techniques.
Integrated with a superconducting quantum interference proximity transistor
(SQUIPT) as a readout set-up, an aluminum (Al)-based TPC calorimeter can
provide a large signal to noise (S/N) ratio $>100$ in the 10~GHz$\cdots$10~THz
frequency range, and a resolving power larger than $10^2$ below 50~mK for THz
photons. In the bolometric operation, electrical NEP of
$\sim10^{-22}$~W$/\sqrt{\text{Hz}}$ is predicted at 50 mK. This device can be
attractive as a cryogenic single-photon sensor operating in the giga- and
terahertz regime, with applications in dark matter searches.
