The resection of brain tumors beneath eloquent areas of the human brain requires precise delineation of eloquent areas for maximum removal of tumor mass while minimizing the risk for postoperative functional deficits. Non-invasive mapping of eloquent areas can be carried out by intraoperative thermal imaging since neural activity alters the cortical temperature distribution. These characteristic changes in cortical temperature can be modeled by a response function. A prominent choice for this response function is the haemodynamic response function. However, the signal is typically superimposed by various effects such as motion artifacts, physiological effects, sensor drifts as well as autoregulation which have to be compensated. In this paper, we contribute a regularized semiparametric regression framework that recognizes the response function while it compensates for arbitrary background signals. We achieve this by learning a tailored L2 penalty that basically regularizes the estimated background signal such that it doesn’t comprise the characteristics of the response function. The evaluation of this approach is carried out by augmented semisynthetic resting-state- as well as intraoperative thermal imaging data.