If that`s 16Aon the 12v rail, I`d go for the 9600GT, it`s by far the fastest on your list with the 9600GSO next and the 4670 last.
The 9600GT draws 60W under load (5A) and the 4670 48W (4A) with the GSO inbetween.
Find out how much power it has on the 12v rail!
As I said, if it has 16A then any of the cards mentioned will run on it, if it`s less that 16A I`d go for the 4670 but you`ll take quite a performance hit:
Don't buy 512mb version of 9600gso. If it's 384mb/768mb, it's ok. 512mb version have 48 shaders G94 based while latter are G92 with 96 shaders. So 512mb 9600gso performs about 70% of 9600gt.
If you'd upgrade you psu, best option is HD4830 at $90, better than all mentioned here; otherwise just get 4670.
Uhm time out!!!! I do NOT agree that a PSU with 16 amps will run a 9600gt. I've got a slightly overclocked 9600gt and it wanted 26 amps if I'm not mistaken. The 4670 would be the best of those 3 for a low power solution. It's about the same speed as the 9600gso, but requires no power connection. So probably best card I would personally take a chance on with a psu like that.
As far as temps, if you are concerned with that, what I did when I got my 9600gt was to get a high flow pci slot cooler fan and mounted in the bays below the card that way a lot of hot air should be pulled off the card and sucked out the back of the case. Might be a good route to go for little cash.
As far as the 9600 gso card, if you do go that route, check the specs as most of them lately seem to be ddr2 cards which would be crippled compared to the other cards your looking at.
I have an HD 4670, just to note. HD 4670 takes a bit less power than the 9600GSO, performance is very close to the same. I don't know where you heard the 4670 is a hot card..... mine's cold. Like.... really cold (load is <40 degrees). And my case isn't well-ventilated, just two 80mm fans (and poor ones at that).