I still recommend a GTX460, hands down, it's the best value (meaning, performance to cost ratio). Yes, I own one, but this is not why I am recommending it to you. The reason I think it fits the bill for you is, firstly, the price, it can't be beat for what you're getting. Under load, the GTX460 hits about 66C (but I don't ever go over 55C) after 1 hour of 3dMark Batch Size test, vs the HD6870 which hits 82C, performance wise, well, that's hard to guess given your set-up, but I'd say it would be around similar outcome, so, why not go with the least expensive option?
Don't forget, the GTX460 can also do CUDA (may be a benefit to you if you take advantage of it, as I do for my HTPC functions). It's great in games, and awesome for HD movies.
Other than that, it's really all about personal taste and brand loyalty. I don't really care what I own as long as it has the right value for my needs. In this case, the 460 did if for me hands down. I seriously have no complaints. Great drivers, great product and that's what matters. The HD6870 is a good product too, though.