The barrel section of the novel MIP Timing Detector (MTD) will be constructed as part of the upgrade of the CMS experiment to provide a time resolution for single charged tracks in the range of 30-60 ps using LYSO:Ce crystal arrays read out with Silicon Photomultipliers (SiPMs). A major challenge for the operation of such a detector is the extremely high radiation level, of about 2 × 1014 1 MeV(Si) Eqv. n/cm2, that will be integrated over a decade of operation of the High Luminosity Large Hadron Collider (HL-LHC). Silicon Photomultipliers exposed to this level of radiation have shown a strong increase in dark count rate and radiation damage effects that also impact their gain and photon detection efficiency. For this reason during operations the whole detector is cooled down to about -35°C. In this paper we illustrate an innovative and cost-effective solution to mitigate the impact of radiation damage on the timing performance of the detector, by integrating small thermo-electric coolers (TECs) on the back of the SiPM package. This additional feature, fully integrated as part of the SiPM array, enables a further decrease in operating temperature down to about -45°C. This leads to a reduction by a factor of about two in the dark count rate without requiring additional power budget, since the power required by the TEC is almost entirely offset by a decrease in the power required for the SiPM operation due to leakage current. In addition, the operation of the TECs with reversed polarity during technical stops of the accelerator can raise the temperature of the SiPMs up to 60°C (about 50°C higher than the rest of the detector), thus accelerating the annealing of radiation damage effects and partly recovering the SiPM performance.