  We measure the temperature dependence of the two-photon absorption and
optical Kerr nonlinearity of a silicon waveguide over a range of temperatures
from 5.5 to 300 K at a wavelength of 1.55 {\mu}m. The two-photon absorption
coefficient is calculated from the power dependent transmission of a 4.9 ps
pulse. We observed a nearly two-fold decrease in the two-photon absorption
coefficient from 0.76 cm/GW at 300K to 0.42 cm/GW at 5.5 K. The Kerr
nonlinearity is inferred from the self-phase modulation induced spectral
broadening of the transmitted pulse. A smaller reduction in Kerr nonlinearity
from 5.2E-18 m^2/W at 300 K to 3.9E-18 m^2/W at 5.5 K is found. The increased
ratio of Kerr to absorptive nonlinearity at low temperatures indicates an
improved operation of devices that make use of a nonlinear phase shift, such as
optical switches or parametric photon-pair sources. We examine how the
heralding efficiency of a photon-pair source will change at low temperature. In
addition, the modelling and experimental techniques developed can readily be
extended to other wavelengths or materials of interest.
