Drats! Just my luck - any other recommendations for the socket 478?
Pentium Ms are Socket 479 machines (although even Intel themselves can't get it right, since it's 479 pins, 1 not used). There should be Shenzhen dealers who can sell you a Pentium-M 770 (the 2.13GHz model) for less than 20 USD including shipping off evilbay. The 770s were popular chips for the higher end ThinkPad T42p/T43p models back in the days.
The thing to watch out for on the Dothans? The 533MHz FSB models (the ones that ends in 0) produces 6w more heat versus the 400MHz models (the ones that end in 5). If you are thinking about using one to replace something like a Dothan based Celeron-M 350, that's an extra 6 watts TDP to compensate for....so make sure that you have thermal handling capacity for it, or if its not a partucularly heavily loaded machine, enable speedstep/ ondemand governor so it'll manage thermals accordingly. If you feel particularly brave there used to be a linux util called phc that lets you undervolt Pentium-M CPUs for greater efficiency.