  Thermal fluctuations play an increasingly important role in micromagnetic
research relevant for various biomedical and other technological applications.
Until now, it was deemed necessary to use a time stepping algorithm with a
fixed time step in order to perform micromagnetic simulations at nonzero
temperatures. However, Berkov and Gorn have shown that the drift term which
generally appears when solving stochastic differential equations can only
influence the length of the magnetization. This quantity is however fixed in
the case of the stochastic Landau-Lifshitz-Gilbert equation. In this paper, we
exploit this fact to straightforwardly extend existing high order solvers with
an adaptive time stepping algorithm. We implemented the presented methods in
the freely available GPU-accelerated micromagnetic software package MuMax3 and
used it to extensively validate the presented methods. Next to the advantage of
having control over the error tolerance, we report a twenty fold speedup
without a loss of accuracy, when using the presented methods as compared to the
hereto best practice of using Heun's solver with a small fixed time step.
