An engine stop determination device comprising: an engine for driving a wheel (6R/6L); vehicle state detection means (D1-D6) for detecting the state of the vehicle; and stop determination means that makes an engine stop determination based on a detected state of the vehicle for determining whether to permit an operation stop of the engine or not; wherein: the engine includes a cooling system, and the cooling system comprises: a first coolant route for circulating coolant between a water jacket of the engine and a heater core; a second coolant route formed to merge with the first coolant route between the water jacket and an upstream side of the heater core and being for circulating the coolant between a waste heat recovery unit and the heater core; coolant force-feed means being able to circulate the coolant in the first coolant route and the second coolant route even when the engine is in an operation stop; a shutoff valve provided on the first coolant route and being opened and closed between the water jacket and a merging point with the second coolant route; a first water-temperature sensor provided in the water jacket or between the water jacket and the shutoff valve on the first coolant route; and a second water-temperature sensor provided between the merging point on the second coolant route with the first coolant route and the heater core; and the stop determination means: performs the engine stop determination based on coolant temperatures (thw1, thw2) detected by the first water-temperature sensor and the second water-temperature sensor, and in making the engine stop determination, selectively uses the coolant temperatures (thw1, thw2) detected by the first water-temperature sensor and the second water-temperature sensor in dependence on whether a heater unit including the heater core is in an operation state or in an out-of-operation state, wherein when the state of the vehicle satisfies predetermined conditions and when the heater unit is in an operation state, the stop determination means permits the operation stop of the engine if the coolant temperature detected by the first water-temperature sensor is greater than or equal to a first threshold value and if the coolant temperature detected by the second water-temperature sensor is greater than or equal to a second threshold value. an engine for driving a wheel (6R/6L); vehicle state detection means (D1-D6) for detecting the state of the vehicle; and stop determination means that makes an engine stop determination based on a detected state of the vehicle for determining whether to permit an operation stop of the engine or not; wherein: the engine includes a cooling system, and the cooling system comprises: a first coolant route for circulating coolant between a water jacket of the engine and a heater core; a second coolant route formed to merge with the first coolant route between the water jacket and an upstream side of the heater core and being for circulating the coolant between a waste heat recovery unit and the heater core; coolant force-feed means being able to circulate the coolant in the first coolant route and the second coolant route even when the engine is in an operation stop; a shutoff valve provided on the first coolant route and being opened and closed between the water jacket and a merging point with the second coolant route; a first water-temperature sensor provided in the water jacket or between the water jacket and the shutoff valve on the first coolant route; and a second water-temperature sensor provided between the merging point on the second coolant route with the first coolant route and the heater core; and the stop determination means: performs the engine stop determination based on coolant temperatures (thw1, thw2) detected by the first water-temperature sensor and the second water-temperature sensor, and in making the engine stop determination, selectively uses the coolant temperatures (thw1, thw2) detected by the first water-temperature sensor and the second water-temperature sensor in dependence on whether a heater unit including the heater core is in an operation state or in an out-of-operation state, wherein when the state of the vehicle satisfies predetermined conditions and when the heater unit is in an operation state, the stop determination means permits the operation stop of the engine if the coolant temperature detected by the first water-temperature sensor is greater than or equal to a first threshold value and if the coolant temperature detected by the second water-temperature sensor is greater than or equal to a second threshold value. performs the engine stop determination based on coolant temperatures (thw1, thw2) detected by the first water-temperature sensor and the second water-temperature sensor, and in making the engine stop determination, selectively uses the coolant temperatures (thw1, thw2) detected by the first water-temperature sensor and the second water-temperature sensor in dependence on whether a heater unit including the heater core is in an operation state or in an out-of-operation state, wherein when the state of the vehicle satisfies predetermined conditions and when the heater unit is in an operation state, the stop determination means permits the operation stop of the engine if the coolant temperature detected by the first water-temperature sensor is greater than or equal to a first threshold value and if the coolant temperature detected by the second water-temperature sensor is greater than or equal to a second threshold value.