Methods, apparatus and systems for reducing engine idling of fuel-driven equipment, for example found on a wellsite and/or including hydraulic pumping systems are provided. In particular, systems and methods are provided for controlling the starting and shutdown of equipment powered by a fuel-driven engine, the system comprising of an energy accumulator comprising or consisting of one or more supercapacitors. The transmission, transmission fluid, or other components can be warmed to prolong time between engine restarts.