Nonlinear optical microscopy is a powerful label-free imaging technology, providing biochem-ical and structural information in living cells and tissues. A possible drawback is photodamageinduced by high-power ultrashort laser pulses. Here we present an experimental study on thou-sands of HeLa cells, to characterize the damage induced by focused femtosecond near-infraredlaser pulses as a function of laser power, scanning speed and exposure time, in both wide-field andpoint-scanning illumination configurations. Our data-driven approach offers an interpretation ofthe underlying damage mechanisms and provides a predictive model that estimates its probabilityand extension and a safety limit for the working conditions in nonlinear optical microscopy. Inparticular, we demonstrate that cells can withstand high temperatures for a short amount of time,while they die if exposed for longer times to mild temperatures. It is thus better to illuminatethe samples with high irradiances: thanks to the nonlinear imaging mechanism, much strongersignals will be generated, enabling fast imaging and thus avoiding sample photodamage.