Do you have any evidence that all government spending produces sustainable growth? If you turn down the thermostat in a government building, does that saving damage the economy?
It's not about sustainable growth, it's about supporting an economy under very specific circumstances in the aftermath of, in this case, a financial shock. Specifically:
-- There are significant unused resources in the economy (essentially a given after a major recession).
-- Private sector actors (households, businesses) are all constrained; in this case by balance sheets and a need to pay off debt.
-- Interest rates are at the zero lower bound meaning conventional monetary policy has no traction.
-- Fiscal Multipliers are > 1 (In fact substantially greater than 1 is more or less agreed by everyone now, at least in hindsight. See the IMF here for example
https://www.imf.org/external/pubs/ft/wp/2013/wp1301.pdf)
Your thermostat example is (obviously) problematic given that any effect would be unnoticeable. But lets say we can switch of heating in all government buildings and having employees wear extra clothing has no effect on productivity.
If the saving is £50m a year the power companies just lost £50m of income. If the fiscal multiplier is 1.3 the economy just lost £65m aggregate demand. Suppose the power company in response cancels some orders for new plant and this send the already struggling local supplier bankrupt? (i.e. hysteresis effects).
But let me put the question the other way.
Given all the above and the real terms negative cost of borrowing lets say Parliament has given you £5bn of stimulus spending. We know that simply spending that money will have economic benefits (see the success of the limited Obama stimulus) but can you think of things to do that might have longer term benefits as well?