I have to rewrite my answer. It's true that thrust is a basic part of the equation that I have left out.
As we know, thrust decreases as Temp and/or Altitude increase. The lower the thrust, the lower is the momentum created by the sudden engine failure. So we need less rudder efficacy to control the aircraft. But is also true that the rudder will need more air speed to control the aircraft's momentum.
So what we need to know know is which of the 2 (thrust or rudder) will have a bigger influence, as DA (Density Altitude) increases.
In Jet Turbine aircraft minimum control speed DECREASE with altitude, this means that in jets, with increasing altitude, we lose more thrust capability than rudder aerodynamical capability. I remeber that in Airbus FBW aircraft (320/330 and 340) you could say that Vmca decreased 1 Kts per each 1000ft increase in Airfield's elevation. The variation in Vmcg in Airbus FBW planes is very similar, but at higher altitudes it decreases almost 2 Kts per 1000ft.
I'm trying to find out how does this thing work with Temp.
Hope this clears my previous mistake, think I was talking more about V1 (that is what I have in mind when I talk about Vmcg) rather than Vmc.
Thanks for watching over my shoulder EnzoC!!!