  We propose a scheme utilizing ideas from infinite dimensional compressed
sensing for thermal source localization. Using the soft recovery framework of
one of the authors, we provide rigorous theoretical guarantees for the recovery
performance. In particular, we extend the framework in order to also include
noisy measurements. Further, we conduct numerical experiments, showing that our
proposed method has strong performance, in a wide range of settings. These
include scenarios with few sensors, off-grid source positioning and high noise
levels, both in one and two dimensions.
