The superconductor-ferromagnet thermoelectric detector (SFTED) is a novel ultrasensitive radiation detector based on the giant thermoelectric effect in superconductor-ferromagnet tunnel junctions. We demonstrate analytical models and solutions in the time domain for a SFTED operated as a microcalorimeter (pulse excitation), in the linear small-signal limit. Based on these solutions, the signal current and temperature pulse response were studied for two different electrical circuit models, providing design conditions for stable and non-oscillatory response.