Hybrid construction machine

A hybrid construction machine comprising:

• an engine;
• an electric motor/generator that assists power of the engine during power running and generates electricity during regenerative braking;
• a hydraulic pump unit that is driven by the power of the engine and delivers a hydraulic fluid;
• an electricity storage device;
• a power converter that converts direct-current power that has been received from the electricity storage device during the power running into alternating-current power and supply the alternating-current power to the electric motor/generator, the power converter converting the alternating-current power that the electric motor/generator has generated into direct-current power and supplying the direct-current power to the electricity storage device;
• a temperature regulator that regulates a temperature of the electricity storage device;
• and
• a control unit that executes at least one of first control, second control, and third control in accordance with a charge/discharge history of the electricity storage device, the first control controlling the temperature regulator so that the temperature of the electricity storage device increases, the second control controlling the power converter so that the power that is output from the power converter is reduced, the third control controlling the hydraulic pump unit so that a flow rate of the fluid delivered from the hydraulic pump unit is reduced.