Last update time for entity

Community, hello.

What property should provide custom component class (class TionClimateDevice(ClimateEntity): for example) to provide last update time at UI?
I have climate component with

def should_poll(self):
        return False

and call self.async_write_ha_state() from update function and sensor with should_poll == True.
Sensor value and climate state updates correctly, but for both cases last update in UI is a time since Home Assistant start.