The present work is concerned with the stabilization of a general class of time-varying linear parabolic equations by means of a finite-dimensional receding horizon control (RHC). The stability and suboptimality of the unconstrained receding horizon framework are studied. The analysis allows the choice of the squared l(1)-norm as control cost. This leads to a nonsmooth infinite horizon problem which provides stabilizing optimal controls with a low number of active actuators over time. Numerical experiments are given which validate the theoretical results and illustrate the qualitative differences between the l(1)- and l(2)-control costs.