Tl$_2$LiYCl$_6$:Ce (TLYC) is a new dual-detection elpasolite scintillator that can detect and distinguish between gamma rays and neutrons using pulse-shape discrimination (PSD). It has a higher density and Z-number than the more mature and well-known elpasolite Cs$_2$LiYCl$_6$:Ce (CLYC), causing it to have a significantly better gamma-ray stopping power. These properties make TLYC an attractive alternative to CLYC for resource-constrained applications where size and weight are important, such as space or national security applications. Such applications may be subjected to a wide range of temperatures, and therefore TLYCs performance was characterized for the first time over a temperature range of -20$^{circ}$C to +50$^{circ}$C in 10$^{circ}$C increments. TLYCs thermal response effects on light-output linearity with energy, gamma-ray photopeak energy resolution, detected neutron energy, pulse shapes, and figure of merit is analyzed and reported. The light output of TLYC was found to be linear with energy over the tested temperature range and was observed to decrease with increasing temperature. The decay time of the scintillation light output was observed to decrease with decreasing temperature at short times, leading to a decreasing PSD figure of merit. The gamma-ray photopeak energy resolution was also observed to degrade with decreasing temperature, due to an asymmetric broadening of the photopeak at low temperatures.
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