GR3 runs on my 15.4" Toshiba Satellite A-215 (AMD Turion X2 64 1.6, ATi graphics, 4 GB RAM, Windows 7 Pro. 32-bit)
I don't have much of an issue. If I'm tracking several storms (like I did when the last outbreak occurred), the computer does warm up a bit, but as long as I don't animate more than one or two windows (depending on how many windows I have open of GR3) the computer runs smoothly.
I've had trial versions of GR3 run on the first gen Acer Aspire One netbooks before (Windows XP)…though I wouldn't recommend running multiple windows of GR3 at once, maybe just a couple - at least on the older Atom chips.