  We develop a set of kinetic equations for hydrodynamic fluctuations which are
equivalent to nonlinear hydrodynamics with noise. The hydro-kinetic equations
can be coupled to existing second order hydrodynamic codes to incorporate the
physics of these fluctuations. We first show that the kinetic response
precisely reproduces the renormalization of the shear viscosity and the
fractional power ($\propto \omega^{3/2}$) which characterizes equilibrium
correlators of energy and momentum for a static fluid. Then we use the
hydro-kinetic equations to analyze thermal fluctuations for a Bjorken
expansion, evaluating the contribution of thermal noise from the earliest
moments and at late times. In the Bjorken case, the solution to the kinetic
equations determines the coefficient of the first fractional power of the
gradient expansion ($\propto 1/(\tau T)^{3/2}$) for the expanding system.
Numerically, we find that the contribution to the longitudinal pressure from
hydrodynamic fluctuations is larger than second order hydrodynamics for typical
medium parameters used to simulate heavy ion collisions.
