If the Asian networking out of the box specialists NorhTec are to be believed the answer is very low indeed: how does $85 (£41) sound? Remarkably that is how much the new NorhTec MicroClient JrSX is set to cost, making it what must be the lowest priced Linux powered thin client PC around.
According to LinuxDevices the MicroClient JrSX is a 300MHz Vortex86SX system-on-chip device, ultra low power it only consumes 0.9W at 300MHz. It includes CompactFlash and 2.5" hard drive storage as well as 10/100Mbps Ethernet, 128Mb DDR RAM, triple USB 2 sockets and all in a box measuring 115x115x35mm which weighs 505gm. The size and weight making it ideal for attaching directly to the back of a flat panel display, which is made even easier by the inclusion of VESA mounting holes on the chassis.
Because of the ultra low power requirement the MicroClient is fan-less, being passively cooled but not adverse to operating in areas of high temperature or humidity for that matter. McDonalds Canada is said to be a customer for just this reason. As far as Linux is concerned, NorhTec reckon it can run any distribution that is compiled to support floating point emulation. Obviously you don't get bells and whistles at this price point, but throw something like Puppy Linux at it and you do get one of the cheapest fully functional PCs on the planet.