Its well known that using heat in a car is almost free (see for example here). It is also known that using the heat can reduce the engine temperature which otherwise needs to rely on water cooling. Since the water cooling has a price it is presumable that this would consume gas, possibly more gas then the cost of using the heat itself.
So my question is whether its actually more gas efficient to use the heat in your car then have it off and if so how big an impact can this have on gas efficiency? How big an impact this is, is also likely a function of the outside temperature, though I understand its likely hard to get that data...
Note: After forming this question I saw the same possibility posed in an answer to the linked question by JuannStrauss.