PC
The most significant requirements on the PC itself are probably size and cooling, and connecting enough peripherals. Small size helps the PC fit into cabinets, but putting the PC in a closed cabinet puts it in a heat pocket where the inlet cooling air will be at temperatures higher than the usual ambient air used to cool the system. You have to address those issues, but have a wide range of options for how you do that — for example:
Thin client — Some years ago Sun, Oracle, and others made a fuss about what they called thin client computing, with the idea being that you’d run all applications on a remote server, or download them from the server to execute on the local machine but keep all programs and storage remote. Either way, you’d need little more than a processor, memory, and display locally, not the rich set of equipment that forms a PC. This is probably the smallest option for a Kitchen PC, but it requires you implement the remote server to support it. Many of the companies that used to build thin clients have gone out of business, but if you’re running Linux you could put just enough hardware behind an LCD display to run the XWindows server, and then host all the rest of your applications on a backend Linux server.
Even if you’re willing and able to write all the necessary software to make this approach work, and so minimize the PC hardware, you still need to figure out how to connect the secondary displays, if any, peripherals, sensors, and networks. Just the connectors and adapter cards required can be more than what’s available on a thin client PC.
Laptop or tablet PC — The compact packaging and integrated display in a laptop or tablet PC works well in any restricted-size application, including the Kitchen PC, and the pen interface on a tablet PC could eliminate the need for a keyboard. Neither form factor will be usable mounted under a cabinet, however, which implies the PC would have to sit on a counter. Power and data connections become a problem in that context, and the limited interfaces on both form factors may not provide what’s necessary without a docking station or port replicator. Either accessory will add cost, take more space, and still not solve the problems you encounter placing the PC on a counter.
Shoebox or desktop PC — A small form factor PC could be the ideal package for a Kitchen PC, because it combines some of the flexibility of a full desktop configuration with the small size that will help you integrate the unit into a cabinet. A desktop is fine too, if you have the space — perhaps inside an island in the middle of a large kitchen.
Slow the machine and use a power-efficient processor — Both the clock rate and the underlying design and fabrication technology of the processor have direct impacts on the power consumed by the processor. High processor clock rates not only consume more power directly, they also tend to be accompanied by faster front side buses which increase the power consumed by the chipset and the memories. Using the slowest machine possible, and using a machine incorporating mobile or other low-power technology, will reduce the power consumption.
Remove excess hardware — All hardware generates heat when there’s power applied, so making sure the machine has only the hardware required will eliminate unnecessary heat produced from otherwise unused hardware. The list of hardware you can likely remove includes excess memory, all disks besides the primary one, high-performance video cards, floppy disks, and optical drives.
Employ aggressive power management — Desktop systems rarely apply the Advanced Configuration and Power Interface (ACPI) technology as aggressively as laptops, using the S1 suspend state instead of S3, for example, and rarely throttling the processor based on thermal limits, but it can be. ACPI helps laptops by extending battery life; doing so in your Kitchen PC helps by reducing power dissipation.
Venting cool air into and hot air out of the cabinet will be far more effective a heat management approach. Assuming you put the PC in the bottom of the cabinet (the heat source in the figure), Figure 3 shows the two fundamental approaches to venting the cabinet. Both build on the normal bottom-to-top convective air flow generated by the hot air; one vents the air to the side, while the other vents into the attic. Both could use a grid of small, hidden holes to bring in cool air from the bottom.
Neither approach is problem free. Venting to the side not only requires a side opening into the room, it requires you make holes in the side of the cabinet. Making holes on the side of the cabinet that actually look acceptable to you (and, perhaps more importantly, to the next buyer of the place) could be hard. Venting to the top avoids the cosmetic issues, but requires you maintain relatively unimpeded airflow all the way up the cabinet and into the attic. You could simply drill holes in the shelves and the top; the bigger problem is the potential loss of shelf space, since if you then cover the holes they stop functioning. Alternatively, you could build a rectangular duct running up the back or side of the cabinet, minimizing the space loss and preventing accidental obstruction of the airflow path.

FIGURE 3: Cooling paths