Oenophiles are aware that the temperature at the time of drinking can profoundly shape wine’s sensory attributes. Wine is usually served and drunk below room temperature but warms up after pouring due to heat exchange with warmer surroundings. This study investigates how quickly wine warms up in a wine glass and identifies the relevant heating effects. A numerical simulation using conjugate heat transfer is established, representing the complex multi-physical process. Experiments are conducted to validate the simulation. It is shown that the simulation must take into account thermal conduction, convection, and even radiation to provide accurate results. Without simulating radiation and convection of the room air, the predicted temperature is off by 66.3% or 3.3 °C. As warming is independent of the alcohol content, the simulation results are valid for non-sparkling wine types with moderate sugar levels within the considered configuration. A parameter study investigated the temperature increase over time depending on the ambient temperature and the initial wine temperature for 150 mL wine in a medium-sized red wine glass. The results can provide information on preparing a wine to obtain the desired drinking temperature.