Recurrent apneic episodes lead to a decrease in blood oxygen levels and eventually hypoxemia. Persistent hypoxemic SpO \(_2\) values during sleep are linked to severe health risks, including organ damage, heart failure, tachycardia, and shortness of breath. Oxygen desaturation events are usually detected during polysomnography (PSG) in sleep laboratories. A PSG involves a high number of contact-based sensors, which may lead to patient discomfort and biased measurement results. In this work, a contactless camera-based oxygen desaturation monitoring method based on the analysis of multispectral videos is proposed. The method is built on the extraction and analysis of remote photoplethysmography (rPPG) signals at wavelengths of 780 and 940 nm from the forehead and a breath temperature signal via far-infrared (FIR) thermography from the subnasal region. A manual feature extraction is implemented to gather pertinent medical and physiological parameters from the obtained signals. These parameters are used to design a fully connected feed-forward neural network-based classifier, which distinguishes between periods with and without desaturation. A patient dataset consisting of 23 sleep apnea patients is collected for evaluation. The classification accuracy between desaturation events and periods without a desaturation based on the leave-one-patient-out cross-validation metric is 95.4%. The oxygen desaturation index (ODI) is estimated with a mean average error (MAE) of 2.9  \(\frac{events}{hour}\) , while a correct ODI stage prediction is given for 21 of the 23 patients. The regression of the exact SpO \(_2\) value during desaturation results in an MAE of 1.79%.