  We demonstrate strong negative electrothermal feedback accelerating and
linearizing the response of a thermal kinetic inductance detector (TKID). TKIDs
are a proposed highly multiplexable replacement to transition-edge sensors and
measure power through the temperature-dependent resonant frequency of a
superconducting microresonator bolometer. At high readout probe power and probe
frequency detuned from the TKID resonant frequency, we observe electrothermal
feedback loop gain up to $\mathcal L$ $\approx$ 16 through measuring the
reduction of settling time. We also show that the detector response has no
detectable non-linearity over a 38% range of incident power and that the
noise-equivalent power is below the design photon noise.
