The study analyzed 273 patients over 18 years of age with fever of unknown origin (FUO) or inflammation of unknown origin (IUO), where FDG-PET/CT provided a diagnostic benefit in 203 patients (74.4%). The aim was to identify clinical and laboratory variables determining the utility of PET/CT and to develop machine learning models to predict true positive and negative results. Algorithms such as XGBoost, Support Vector Machines, Multilayer Perceptron (MLP), KNN, Random Forest, Decision Tree, Logistic Regression (LR) and Naive Bayes were used, with feature selection by the PowerSHAP method. The best results were achieved by MLP (PR-AUC 0.86) and XGBoost (PR-AUC 0.85), while MLP and LR excelled when combining PR-AUC and accuracy. LR had precision values of 0.75, ROC-AUC of 0.74, PR-AUC of 0.84, precision of 0.85, recall of 0.86, and F1 score of 0.83. PowerSHAP showed that lower procalcitonin and erythrocyte sedimentation rates, longer duration of symptoms, older age, generalized pain, hospitalization, and higher lymphocyte counts were associated with higher PET/CT utility. The MLP and LR models may help select patients who benefit from PET/CT, but further validation is needed.