We study a recently observed gravitational microlensing peak in the V-band light curve of Q2237+0305A using a relatively simple physical model, but one that is highly consistent with the data (the best-fit reduced chi 2 is very close to 1). The source quasar is assumed to be a Newtonian geometrically-thin and optically-thick accretion disk. The disk has an arbitrary orientation, and both blackbody and greybody emission spectra are considered. When the electron-photon scattering plays a role, the greybody spectrum will be a simplified version of the exact one. In our model, the microlensing variability results from the source crossing a caustic straight line. The main goal of our work is to estimate the black hole mass and the mass accretion rate in QSO 2237+0305 as well as to discuss the power and the weakness of the technique, some possible improvements, and future prospects from multifrequency monitoring of new microlensing peaks. We also put into perspective the new methodology and the results on the central engine in QSO 2237+0305. From the fitted microlensing parameters and reasonable dynamical/cosmological constraints, it is concluded that QSO 2237+0305 harbours a central massive black hole: 107 Msun < M < 6 x 108 Msun. While the information about the central dark mass is very interesting, the mass accretion rate is not so well constrained. The typical values of the disk luminosity/Eddington luminosity ratio are in the (1-20)varepsilon range, where varepsilon <= 1 is the emissivity relative to a blackbody and the highest L/LEdd ratio corresponds to the largest deflector motion. Therefore, in order to verify L/LEdd <= 1, a relatively small projected peculiar motion of the lens galaxy and a greybody emission seem to be favored.