Extensional flows of complex fluids are prevalent in everyday lives and specifically in the automotive industry, the examples of which include motor lubrication, manufacturing and painting. Even if the fluid is weakly elastic, the system can exhibit complex flow behaviors due to large strain and strain rates that develop near pinch-off. Here we aim at providing a rapid testing protocol to quantify the extensional rheology of weakly elastic automotive lubricants. This is achieved through an improved Capillary Breakup Extensional Rheometer (CaBER) with better-controlled disc motion and an extra temperature controller. This technique works on imposing a well-controlled step strain to a cylindrical liquid sample between two coaxial discs to initiate the capillary thinning. The temporal evolution of the resulting liquid bridge can be captured using a laser micrometer or a high-speed camera, and is further used to probe the underlying fluid properties. Two commercial 10W-30 motor oils are chosen, which appear to be identically Newtonian in shear flow. However, the capillary thinning measurements show rate-thickening behaviors close to breakup deviating from the Newtonian predictions. This weakly elastic response is understood using the well-established constitutive equations such as Oldroyd-B and second order fluid models with extra non-linear stress terms. Such rate-thickening regions are highly related to a number of automotive applications such as jetting and metal stamping, thus can provide more insights into the complex flow behaviors and to potentially optimize the industrial processes.