How to calculate "mean instant power"?
This isn't a complete answer because the question needs a bit of a clean-up.

The heater is running 1/2 hour then stop for 1h ...

That's a 1.5 hour duty-cycle

... for 6h straight (from 6pm to 6am next day)

6 p.m. to 6 a.m. is not 6 h. You need to fix that.

I need to calculate the mean instant power of that circuit,

Instant power is the power at any single time. This will be 2000 W or zero.
The mean power is the time averaged power.

I went to the conclusion that this value would be nominal power * duty cycle ratio but I'm not sure at all of that.

That's mean power, not &quot;mean instant power&quot;.
Fix the 6 h straight bit and we'll try to answer.