  We introduce a multitree-based adaptive wavelet Galerkin algorithm {for}
space-time discretized linear parabolic partial differential equations,
focusing on time-periodic problems. It is shown that the method converges with
the best possible rate in linear complexity and can be applied for a wide range
of wavelet bases. We discuss the implementational challenges arising from the
Petrov-Galerkin nature of the variational formulation and present numerical
results for the heat and a convection-diffusion-reaction equation.
