I shouldn't have worded it as "going" rather sustaining. And in terms of cars, yes it usually is more fuel demanding to sustain 80 MPH than it is 65 due to wind resistance and general higher RPM's of the engine.
Wind resistance scales as the square of speed. Engine performance is more complex and also depends on gearing, but I doubt that it is linear either. Once you're in top gear going 50+, you can expect a nonlinear dropoff in mileage as speed increases.
Heat transfer rate, however, depends directly on temperature differential times a bunch of things (area, heat transfer coefficient, thickness) which are constant for a given house. So, how much heat is ENTERING the house increases linearly as the outside temperature goes up (assuming constant inside temp).
However, the coefficient of performance of your AC which is removing the heat is NOT linear, and decreases as the temperature differential between the hot and cold sides increases. Which means that as the watts of heat entering your house increase, you have to spend more watts of electricity per watt of heat to pump them back out.
Which is why ground-source heat pumps are so great. The heat entering your house is still determined by air temperature (linear), but the COP of your heat pump will be reasonably constant, since ground temperatures won't increase nearly as quickly.
Of course, electricity is pretty cheap in the US, and ground-source heat pumps are super expensive to install if you don't DIY.