Engine and outboard motor

An engine comprising:

• a combustion chamber in which an air-fuel mixture of air and fuel is combusted;
• a crankshaft which rotates in accordance with a combustion of the air-fuel mixture in the combustion chamber;
• an intake passage which guides a gas toward the combustion chamber;
• a throttle valve which changes a flow rate of the gas supplied from the intake passage to the combustion chamber;
• a fuel injector which injects a fuel into the intake passage or into the combustion chamber;
• an exhaust passage which guides exhaust discharged from the combustion chamber;
• a catalyst disposed inside the exhaust passage;
• a temperature detecting device which detects a temperature of the engine;
• and
• a controller programmed to judge whether or not the engine is overheating based on a detection value of the temperature detecting device and, if the engine is overheating, to control an opening degree of the throttle valve or an injection amount of fuel from the fuel injector to decrease a rotational speed of the crankshaft and to control the injection amount of fuel from the fuel injector to set a target air-fuel ratio to a value richer than a stoichiometric air-fuel ratio.