The investigation of spontaneous and evoked neuronal activity from functional Magnetic Resonance Imaging (fMRI) data has come to play a significant role in deepening our understanding of brain function. As this research trend continues, activity detection methods that can adapt to different activation scenarios must be developed. The present work describes a new method for temporal semi-blind deconvolution of fMRI data; i.e., undo temporal signals from the effect of the Hamodynamic Response Function (HRF), in the absence of information about the timing and duration of neuronal events and under uncertain characterization of cerebral hemodynamics A sequential minimization of two functionals is deployed: the first functional recovers activity signals with sparse transients while the second exploits the retrieved activity moments to estimate the Taylor expansion coefficients of the HRF. These coefficients are inherently linked to two values of interests that characterize the hemodynamics" time-to-peak and the width of the response. We evaluate the performances of the method on synthetic signals before demonstrating its potential on experimental measurements from the visual cortex.