The transient response of least-squares-based multiwavelength pyrometers to rapid temperature changes is modeled. Results are presented for a one-parameter and a four-parameter linear least-squares pyrometer with 31 wavelengths from 500 to 800 nm. The one-parameter response is very similar to the transient response of a two-color pyrometer. The response is more rapid than expected when the target temperature is rising and slower than expected when the target temperature is falling. The four-parameter pyrometer can overfit and indicate erroneous temperatures.