A method of controlling a rate of warm-up of an internal combustion engine fluidly connected to an exhaust system is disclosed. The method includes identifying a cold-start of the engine. The method also includes regulating, in response to the identified cold-start of the engine, an exhaust pressure modulation (EPM) valve arranged in a main exhaust passage of the exhaust system. The main exhaust passage channels engine exhaust gas to the ambient. Such regulation of the EPM valve will restrict a flow of the engine exhaust gas to the ambient and increase exhaust gas backpressure in the exhaust system up to a predetermined pressure value. Furthermore, the subject regulation of the EPM valve will increase a load on and the rate of warm-up of the engine. A vehicle having an engine and a controller programmed to control a rate of the engine's warm-up of according to the method is also disclosed.