  LaB$_3$:Ce crystals have been introduced for radiation imaging in medical
physics, with photomultiplier or single SiPM readout. An R-D was pursued with
1/2" and 1" LaBr3:Ce crystals, from different producers, to realize compact
large area detectors (up to some cm$^2$ area) with SiPM array readout, aiming
at high light yields, good energy resolution, good detector linearity and fast
time response for low-energy X-rays. A natural application was found inside the
FAMU project at RIKEN-RAL muon facility, that aims at a precise measure of the
proton Zemach radius to solve the so-called "proton radius puzzle", triggered
by the recent measure of the proton charge radius at PSI. The goal is the
detection of characteristic X-rays around 130 keV. Other applications may be
foreseen in medical physics, such as PET, and gamma-ray astronomy. A limiting
factor is the gain drift of SiPM arrays with temperature, that give a
deterioration of the detector's FWHM energy resolution. To solve this problem,
a custom NIM module, based on CAEN A7585 digital power supply, was developed.
Test results of the correction of gain drift with temperature for SiPM arrays
from Advansid, Sensl, Hamamatsu will be presented. At the $^{137}$Cs peak, an
energy resolution better than 3% was obtained for a typical LaBr$_3$:Ce
crystal, using Hamamatsu S13461 arrays. This compares well with best available
results obtained with PMTs.
