It's not about how hot it runs - that's affected by the cooler mounted and such, and the GTX470 stock cooler is more effective than the 4870's. It's about how much heat
energy needs to be dissipated. This is where the card's TDP comes into play. The 4870 1GB has a 206W TDP while the GTX470 has a 232W TDP. So while the GTX470 'runs cooler', it actually requires more heat to be dissipated.
(Figures taken from
TPU's GTX470 review)