Bolometric detectors are used in particle physics experiments to search for rare processes, such as neutrinoless double beta decay and dark matter interactions. By operating at cryogenic temperatures, they are able to detect particle energies from a few keV up to several MeV, measuring the temperature rise produced by the energy released. This work focusses on the bolometers of the CUORE experiment, which are made of TeO2 crystals. The response of these detectors is nonlinear with energy and changes with the operating temperature. The noise depends on the working conditions and significantly affects the energy resolution and the detection performances at low energies. We present a software tool to simulate signal and noise of CUORE-like bolometers, including effects generated by operating temperature drifts, nonlinearities and pileups. The simulations agree well with data.