During engine warm-up, a flow regulating unit in a cooling system operates in a fuel efficiency priority mode. In this mode, a head-side cooling water flow rate (Qhd) is regulated to be equal to or smaller than a first upper limit; a block-side cooling water flow rate (Qbk) is regulated to be equal to or smaller than a second upper limit; and cooling water flowing out of a block-side passage and a head-side passage flows mainly into a bypass passage. When a heating request to heat blown air is made during engine warm-up, the regulating unit operates in a heating priority mode. In this mode, Qhd is regulated to be equal to or smaller than a third upper limit; Qbk is regulated to be equal to or smaller than a fourth upper limit; and at least cooling water flowing out of the head-side passage flows into a heat exchanger.