This question is related to the potential SWIFT block that might happen any time soon.
It sounds maybe naive but I was thinking that if we almost all turn down our heating system by ~3° Celsius (compared to our current settings) we could potentially save gas consumption that can be better used for other purposes. What do you think?
It's not naive. Going to "pure" building science (I studied this in uni) the formula for the building heat loss is Q=U.A.dT where dT is the temperature difference between indoors and the outdoors.
If you assume that outdoors is 5°C on average in year, and indoors is 21°C, dT is 16. reducing the indoor temp to 18°C puts the dT at 13.
Since everything else stays the same, you'd expect a 23% decrease in heat loss (Q). And that much less energy need to be replenished.
In the real world buildings are more complicated than that. Also you may risk giving more people diseases and reduce cognitive abilities when things get cold. So perhaps also tell the public to dress warmer and drink more hot fluids.