Our recent success in triggering dendritic flux instabilities in YBa 2 Cu 3 O 7−δ (YBCO) films by applying magnetic fields at ultrahigh rates is followed here by a detailed study of the effect as a function of the field ramp rate,Ḃ a , and temperature, T. We trace the borderline in theḂ aT plane separating regions of smooth, gradual flux penetration and dendritic flux avalanches. In addition, we describe the changes in the dendritic morphology in the instability region as a result of changes in eitherḂ a or T. Our experimental results, showing a monotonic increase of the avalanche threshold field ramp rate with temperature, are discussed in the framework of existing theories. On the basis of these theories we also explain the high stability of YBCO to dendritic avalanches as compared to, e.g., MgB 2 , identifying the flux flow resistivity, rather than any of the thermal parameters, as the main parameter governing the film stability.