(1) Background: The health benefits of extra-virgin olive oil (EVOO), a key component of the Mediterranean diet, are attributed to its polyphenol profile. EVOO is often consumed cooked, and this process may degrade and transform polyphenols. (2) Methods: In this work, we determined how temperature, time, and the interaction between them affects the EVOO polyphenolic profile during a domestic pan-frying process, simulating the cooking conditions of a home kitchen, without the control of light or oxygen. Applying a 22 full factorial design experiment, “Hojiblanca” EVOO was processed at two temperatures (120 °C and 170 °C) either for a short time or a long time, mimicking a domestic process, and polyphenol content was analyzed by UPLC-ESI-QqQ-MS/MS. (3) Results: Temperature degraded the polyphenols of EVOO during the sauté cooking process, whereas time had an effect on some individual phenols, such as hydroxytyrosol, but not on the total phenol content. The polyphenol content decreased by 40% at 120 °C and 75% at 170 °C compared to raw EVOO. (4) Conclusions: Cooked EVOO still meets the parameters of the EU’s health claim.