This research article presents the experimental evaluation of thermal conductivity for hydraulic oil-based hybrid nanolubricants with an aim to enhance the heat transfer potential in engineering applications. The nanolubricant samples were formulated at concentrations ranging from 0.3 to 1.8%. Using transient hot wire method, the thermal conductivity of nanolubricants were evaluated for all the samples from 30 to 80 °C. The maximum enhancement in thermal conductivity was 62.93% for the highest concentration. In this paper, response surface methodology (RSM) and artificial neural network (ANN) have been employed for prediction of the thermal conductivity of nanolubricants. In RSM, analysis of variance (ANOVA) and 3D surface plot techniques were used to determine the significance of the interaction parameters on the output. A new correlation has been proposed to predict the thermal conductivity of the nanolubricants with a R2 value of 0.9992. A combination of concentration and temperature (1.5783 vol% and 72.5695 °C) yielded to the maximum optimal thermal conductivity of 0.204526 Wm−1 K−1. In addition, multilayer perceptron, a type of neural network model, has been trained and tested to predict the thermal conductivity of the nanolubricants. Experiments have revealed that the ANN model consisting of only 10 hidden neurons has been able to achieve an average R2 of 0.98567 and RMSE of 0.02463 thereby establishing its ingenuity. Comparatively, it turned out that the RSM model was slightly more accurate in predicting thermal conductivity than the ANN model.