Thermal pulse literally refers to an episode in which something is hotter for a limited time, something that can occur at various stages of stellar evolution. The term is commonly used for asymptotic giant branch stars, which often go through stages of helium fusion which exhausts the supply enough to cease after a short timespan, i.e., the TP-AGB stage. It often repeats as more helium is produced by an outer shell of hydrogen fusion. Under various circumstances, the fusion may last mere seconds (helium flash), or may last longer, to hundreds of years.
Helium runaway is helium fusion that increases its fusion rate through the heat it creates, quickly depleting the supply.
The term thermal pulse cycle (TPC) is used for the cycle of thermal pulses in an AGB star. The terms late thermal pulse (LTP) and very late thermal pulse (VLTP) are generally used for thermal pulses after the AGB stage (post AGB star).