I'm really not sure if this is the place to start talking about power usage. It's probably part of the engine that nobody wants to fiddle with at this point in development.
My setup is(was) a z77x-ud gigabyte mobo, i5 processor, asus gtx-570 video card. 550W Antec power supply, which is marginal for this hardware at full load. OS is Win7 64bit ultimate.
I've played Civ5 without a problem, and Fallen Enchantress, Divinity 2, Fallout 3 and Skyrim without a hitch.
Since I subscribed to the open Beta of Legendary Heroes, I started to get black screen resets when and after I played FE-LH, as of about 2 weeks ago.
Now, it's just remotely possible that there is a problem developing in my system ... I'm about to put a bigger PSU in to see how that affects things. For the time being I've put another, much lesser video card in (ATI 5570 silent) to the system and it's stabilized - but I think that for a TBS game to use this much power ... is questionable. Normal operating temps here are ~35degrees Celsius cpu and gpu but FE-LH 1.3 pushes those up to >60 degrees. As I said, it seems a LOT of loading for a TBS - particularly if I haven't made a move for 20 minutes and there should not really be any AI calculations taking place. N.B. this has only started after I opted in to the 1.3 beta, but of course that might be coincidental.
*update* I've replaced my 550W PSU with a 750W one and put my GTX 570 back into the box, so far it's stable. Curiously, the GPU temps reported are a few degrees lower with this setup, just sub-60Celsius despite my trying to stress the system by setting everything in basic video options to max.
Still, I found with slightly reduced basic settings the demands on the system dropped dramatically. Either the anti-aliassing or the particle effects really seem to stress the power requirements on my video card immensely with this game.