"by reducing the amount of material the current needs to pass through (reducing heat generated through resistance)"
That is just a little bit backwards. Decreasing LENGTH of the lines would indeed decrease resistance. But the decrease in width and thickness (also part of that die shrink) will very much INCREASE resistance and INCREASE heat output, IF they keep the same voltage. Why do you think operating voltages of these things have dropped from 3.3V down to just one volt now?
In this case, the decrease in area (width x height) of the assorted elements more than offsets the linear decrease length.
And there is a WHOLE lot more to a new process than just transistor widths. Power consumption is going to be driven far more strongly by gate leakage and clock frequency that by simple resistance.
Heck, that is one reason the original Pentium 4 never made it that far: the .13 micron process SUCKED at gate leakage and they never could fix it. That leakage wasn't truely "fixed" until the 65nm process and it was greatly improved upon with the 45nm process.
So, just because AMD has a 45nm process, it doesn't automatically mean it will allow them to make lower TDP parts.
I hope they DO get it right though. Intel tends to become VERY complacent when they don't have a competitor nipping on their heels (or even passing them up like during the P4 days!)