  We construct a determining form for the 2D Rayleigh-B\'enard (RB) system in a
strip with solid horizontal boundaries, in the cases of no-slip and stress-free
boundary conditions. The determining form is an ODE in a Banach space of
trajectories whose steady states comprise the long-time dynamics of the RB
system. In fact, solutions on the global attractor of the RB system can be
further identified through the zeros of a scalar equation to which the ODE
reduces for each initial trajectory. The twist in this work is that the
trajectories are for the velocity field only, which in turn determines the
corresponding trajectories of the temperature.
