I have Amithlon running on my Toshiba laptop. It's only a 500Mhz Celeron with 192Megs of ram but it runs Amithlon great. I've had no problems with overheating but it does kill the battery faster than Windows (probably twice as fast) but I usually have my laptop plugged in when I use it so that's not an issue. The only problem I have with my laptop is that I can't get the sound to work in Amithlon.
The one really nice thing about this laptop is that it has a nice mix of new stuff and legacy stuff. For example it has a DVD drive and a floppy drive (and I'm not talking about being able to pull out the DVD drive to plug in a floppy drive, I have access to both at the same time). It has USB, PS/2, parallel, serial, and modem ports (I just wish it had an ethernet port but that's easily added via PCMCIA). The presence of the floppy drive and legacy ports comes in very handy with Amithlon whereas the DVD and USB allow me to use some more modern technology as well.
I also have WinXP installed with WinUAE but I rarely use that as it's horribly slow (to boot into Windows and then into AmigaOS via WinUAE takes FOREVER).