We investigate limits on the thermal-response time of superconducting
transition-edge microcalorimeters. For operation at 0.1 K, we show tha
t the lower limit on the response time of a superconducting transition
-edge microcalorimeter is of order 1 mu s due to the heat diffusion ti
me, electrical instabilities, the amplifier noise, and the critical cu
rrent of the superconducting film. The response time is not limited by
self-heating effects and is independent of the intended photon energy
. However, design constraints associated with the inductance of the bi
as circuit make it difficult to achieve the fastest response times for
devices with heat capacities high enough for x-ray and gamma-ray dete
ction.