Temperature response functions have been developed to investigate sensor design and divertor heat flux estimation in magnetically confined plasmas. The time-dependent heat flux can be derived by fitting the response function to experimental thermocouple (TC) data. Because the TC signals have a time delay to transit events such as discharge start or additional heat pulse, the time delay is taken into account in a temperature response function. Such a function accurately describes the signal from each TC channel with time delay in a sensor test using a neutral beam injection. Measurement for commercial TCs shows that the time delay is caused by the finite heat capacity of TC wire and contact heat resistance between TC and target surface.