This article presents a comprehensive thermomechanical analysis and failure assessment in the drilling of glass fiber-reinforced polymer (GFRP) composites with different thicknesses using a CNC machine and cemented carbide drill with a diameter of 6 mm and point angles of ϕ = 118°. The temperature distribution through drilling was measured using two techniques. The first technique was based on contactless measurements using an IR Fluke camera. The second was based on contact measurements using two thermocouples inserted inside the drill bit. A Kistler dynamometer was used to measure the cutting forces. The delamination factors at the hole exit and hole entry were quantified by using the image processing technique. Multi-variable regression analysis and surface plots were performed to illustrate the significant coefficients and contribution of the machining variables (i.e., feed, speed, and laminate thickness) on machinability parameters (i.e., the thrust force, torque, temperatures, and delamination). It is concluded that the cutting time, as a function of machining variables, has significant control over the induced temperature and, thus, the force, torque, and delamination factor in drilling GFRP composites. The maximum temperature recorded by the IR camera is lower than that of the instrumented drill because the IR camera cannot directly measure the tool–work interaction zone during the drilling process. At the same cutting condition, it is observed that by increasing the thickness of the specimen, the temperature increased. Increasing the thickness from 2.6 to 7.7 had a significant effect on the heat distribution of the HAZ. At a smaller thickness, increasing the cutting speed from 400 to 1600 rpm decreased the maximum thrust force by 15%. The push-out delaminations of the GFRP laminate were accompanied by edge chipping, spalling, and uncut fibers, which were higher than those of the peel-up delaminations.