A microwave kinetic inductance detector (MKID) is a cutting-edge
superconducting detector, and its principle is based on a superconducting
resonator circuit. The superconducting transition temperature (Tc) of the MKID
is an important parameter because various MKID characterization parameters
depend on it. In this paper, we propose a method to measure the Tc of the MKID
by changing the applied power of the readout microwaves. A small fraction of
the readout power is deposited in the MKID, and the number of quasiparticles in
the MKID increases with this power. Furthermore, the quasiparticle lifetime
decreases with the number of quasiparticles. Therefore, we can measure the
relation between the quasiparticle lifetime and the detector response by
rapidly varying the readout power. From this relation, we estimate the
intrinsic quasiparticle lifetime. This lifetime is theoretically modeled by Tc,
the physical temperature of the MKID device, and other known parameters. We
obtain Tc by comparing the measured lifetime with that acquired using the
theoretical model. Using an MKID fabricated with aluminum, we demonstrate this
method at a 0.3 K operation. The results are consistent with those obtained by
Tc measured by monitoring the transmittance of the readout microwaves with the
variation in the device temperature. The method proposed in this paper is
applicable to other types, such as a hybrid-type MKID.