An adaptive approach is presented to investigate the QT interval response to heart rate variations on a beat-to-beat basis. The relationship between the QT interval and the RR interval is modelled by considering a time-variant system composed of a linear filter followed by a zero-memory nonlinearity approximated by a Taylor expansion. The linear portion describes the influence of previous RR intervals on each QT measurement, while the nonlinear portion expresses how the QT values evolve as a function of the averaged RR measurement at the output of the linear filter. For identification of the unknown system, a Kalman-based procedure is developed that simultaneously estimates all the parameters of the global system. The methodology has been first tested over artificially generated data, showing very good agreement between estimated and theoretical values. Results on data measured over real ECG recordings confirm that the QT interval response is delayed with respect to the RR interval, specially for decelerating heart rate changes. It is also shown that the beat-to-beat evolution of the nonlinearity coefficients is considerably altered when abrupt rate variations occur.