I would not advise putting a processor in a dishwasher. I can think of a few reasons not to do it:
1) Static
2) Rust (inside or out)
3) Heat from the dishwasher (Processors are designed for heat, so I'm not sure on this one)
4) Some soaps could contain chemicals that damage the processor.
5) Hard water deposits
6) Other deposits or the soap creating a bridge
Did you check
Artic Silver's Instructions?
Arctic Silver thermal compound can easily be removed from hardware using the proper cleaners and tools. For general clean-up, a cloth or paper towel will work well. Intricate cleaning can be accomplished with Q-tip swabs. An old toothbrush can often get the compound out of crevices that other tools cannot reach.
The recommended cleaners are:
CPU Core:
Use isopropyl alcohol or acetone (nail polish remover) and a bit of careful rubbing.
(If you use acetone, do a final cleaning with isopropyl alcohol.)
Heatsink:
Use xylene based products (Goof Off, some carburetor cleaners and many brake cleaners.) or mineral spirits.
Remember:
Once you have applied a thermal grease or melted a thermal pad onto a heatsink, it is impossible to remove all of the grease or pad from the microscopic valleys in the heatsink using standard cleaning chemicals and paper or fabric towels. Any subsequent thermal material will be applied over the remnants of the original material.
Never use any oil or petroleum based cleaners (WD-40, citrus based grease removers and many automotive degreasers) on the base of a heatsink. The oil, which is engineered to not evaporate, will fill in the microscopic valleys in the metal and significantly reduce the effectiveness of any subsequently applied thermal compound.
CPU Ceramic:
Use any of the following cleaners.
Any dish detergent (Dawn, Lux, Palmolive, Etc.)
Do not use soap for an automatic dishwasher to clean a CPU.
WD-40, citrus based grease removers (Goo Gone, Etc.)
Xylene based products (Goof Off, some carburetor cleaners and many brake cleaners)
Mineral spirits. (Be careful to keep the mineral spirits away from the core.)
Once the majority of the compound has been removed from the ceramic, small patches remaining on the ceramic can be 'erased' with a soft eraser.
As far as keyboards and dishwashers go. There are a number of keyboards that will survive going through a dishwasher without soap. The good quality IBM keyboards are a good example (however on those, if it is just the keys take those off). A lot of people I know have done this. They have started having some of the newer cheap keyboards die from this, "Oh well, it was time to replace it anyways." If you are going to buy a new keyboard anyways, it doesn't hurt to give it a try. Basically, it comes down to the issue of whether the board inside the keyboard will survive it. If you have a fancy keyboard with all that extra stuff on it, the chances of it surviving are much less. Some people take the safer approach of opening up the keyboard, taking out the board, and then running it through the dishwasher. I haven't heard of that hurting any keyboards.
If it is only your keys that are dirty and you have a keyboard where the keys are easy to take on and off, you can just take the keys off and put them in a bowl with hand dish soap.
Those same points I made on the processor could be made about a keyboard too, but a CPU is a lot more sensitive of a part.
As far as the Artic Silver conductivity issue. The first Artic Silver was highly conductive, but they solved that issue. However, one would still not to have it touching
the bridges or traces.
Negligible electrical conductivity.
Arctic Silver 3 was formulated to conduct heat, not electricity. It is only electrically conductive in a thin layer under extreme compression.
(While much safer than electrically conductive silver and copper greases, Arctic Silver 3 should be kept away from electrical traces, pins, and leads. The compound is slightly capacitive and could potentially cause problems if it bridged two close-proximity electrical paths.)