In cases where a control device determines that a load is continuously less than a predetermined value for a predetermined period, the control device executes a first control to maintain the engine speed at a first rotation speed or higher, and when the control device determines that the load reached the predetermined value within the predetermined time, the control device executes a second control to maintain the engine speed at a second rotation speed or higher, which is higher than the first rotation speed. This provides a control device for an engine and an engine, which can restrain activation of an oil pressure switch attributed to an oil temperature.