We present for the neutron-star low-mass X-ray binary 4U 1636-53, and for the first time for any source of kilohertz quasi-periodic oscillations (kHz QPOs), the two-dimensional behaviour of the fractional rms amplitude of the kHz QPOs in the parameter space defined by QPO frequency and photon energy. We find that the rms amplitude of the lower kHz QPO increases with energy up to similar to 12 keV and then decreases at higher energies, while the rms amplitude of the upper kHz QPO either continues increasing or levels off at high energies. The rms amplitude of the lower kHz QPO increases and then decreases with frequency, peaking at similar to 760 Hz, while the amplitude of the upper kHz QPO decreases with frequency, with a local maximum at around similar to 770 Hz, and is consistent with becoming zero at the sameQPOfrequency, similar to 1400 Hz, in all energy bands, thus constraining the neutron-star mass at M-NS <= 1.6M(circle dot), under the assumption that this QPO reflects the Keplerian frequency at the inner edge of the accretion disc. We show that the slope of the rms energy spectrum is connected to the changing properties of the kHz QPOs in different energy bands as its frequencies change. Finally, we discuss a possible mechanism responsible for the radiative properties of the kHz QPOs and, based on a model in which the QPO arises from oscillations in a Comptonizing cloud of hot electrons, we show that the properties of the kHz QPOs can constrain the thermodynamic properties of the inner accretion flow.