How important is power consumption?
As long as your PSU can handle the load, that really is up to you - whether or not you are concerned about the added cost or are environmentally conscious
Heat?
That is a different issue - heat is the enemy of any electrical system, especially a PC. It is a good reason to avoid the 4870 and go with more modern cards that operate at lower temperatures.
DirectX 11?
Not that important today - but over time its importance will increase.
I recommend the GTX 460 768MB card. It is a solid card that can be found at a discount right now because it is being replaced by the GTX 550 Ti, but the new card is slower. The 768MB version of the GTX 460 is only slightly slower than the 1GB version, but costs substantially less. See the slight performance difference in this article:
http://www.tomshardware.com/reviews/geforce-gtx-460-gf1...
That review also shows that the GTX 460 768MB card is about 20% faster than the HD 5770. It also shows that it uses about the same power as the HD 5770 at idle, about 10% more power under full load, but runs about 20% cooler at idle and under load.
Note that on the THG Best Card for the Money article linked below, the GTX 460 1 GB is one of the cards recommended at the $200 price level. This card is almost as fast and as shown in the review above, and costs quite a bit less..
http://www.tomshardware.com/reviews/best-gaming-graphic...
For a specific card, I recommend the MSI Twin Frozr because of its effective but quiet heatsink/fan, factory overclock, and good price – only $130 after rebate.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
You can find more information about determining system requirements and limitations when upgrading video cards choosing features at:
http://www.upgradevideocards.com/brands.html