A study on the velocity sensitivity and intrinsic thermoacoustic stability of a laminar, premixed, Bunsen-type flame is carried out. Direct numerical simulation (DNS) of the flame, placed in an acoustically anechoic environment and subjected to broad-band, low-amplitude acoustic forcing, generates time series of fluctuating heat release rate, velocities and pressure. The time series data is post-processed with system identification to estimate the impulse response and transfer function of the flame. The associated frequency response is validated against experiment with good accuracy. DNS results obtained with acoustic excitation from the inlet or outlet boundary, respectively, confirm that the flame responds predominantly to perturbations of velocity. The stability of eigenmodes related to intrinsic thermoacoustic feedback is investigated with a network model. Both stable and unstable intrinsic thermoacoustic modes are predicted, depending on details of the configuration. The predicted modes are directly observed in direct numerical simulations, with good agreement in frequencies and stability.