An engine warming system for a machine is disclosed. The engine warming system may have a first engine and a second engine each connected to a dedicated first heat exchanger and a second heat exchanger, respectively. The engine warming system may also have a common heat exchanger connected to both the first and second engines to transfer heat between coolant flows from the first and second engines. Further, the engine warming system may have a first pump and a second pump driven by the first engine and second engine, respectively, to circulate coolant from the first and second engines through the common heat exchanger. The engine warming system may also have at least one coolant pump driven by power generated by at least one of the first and second engines, to circulate coolant from a non-operational one of the first and second engines through the common heat exchanger.