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The Cryogenic Underground Observatory for Rare Events (CUORE) is the mostsensitive experiment searching for neutrinoless double-beta decay($0\nu\beta\beta$) in $^{130}\text{Te}$. CUORE uses a cryogenic array of 988TeO$_2$ calorimeters operated at $\sim$10 mK with a total mass of 741 kg. Tofurther increase the sensitivity, the detector response must be wellunderstood. Here, we present a non-linear thermal model for the CUOREexperiment on a detector-by-detector basis. We have examined both equilibriumand dynamic electro-thermal models of detectors by numerically fittingnon-linear differential equations to the detector data of a subset of CUOREchannels which are well characterized and representative of all channels. Wedemonstrate that the hot-electron effect and electric-field dependence ofresistance in NTD-Ge thermistors alone are inadequate to describe ourdetectors' energy dependent pulse shapes. We introduce an empiricalsecond-order correction factor in the exponential temperature dependence of thethermistor, which produces excellent agreement with energy-dependent pulseshape data up to 6 MeV. We also present a noise analysis using the fittedthermal parameters and show that the intrinsic thermal noise is negligiblecompared to the observed noise for our detectors.

An Energy-dependent Electro-thermal Response Model of CUORE Cryogenic Calorimeter