Cleaning computer cables In the dishwasher
People do all kinds of things that aren't a good idea. If you read the answers on your linked question, you'll see that some people managed to get away with it and some didn't.
Dishwasher Use
Personally, I wouldn't use a dishwasher at all for cables (or other electrical/electronic components). The detergent requires very hot water to thoroughly dissolve and rinse, and can leave residue. It also tends to be a little corrosive. The plastic won't melt at dishwasher temperatures (unless a cable falls near the drying element), but it can leach out some of the plasticizer and make the plastic more brittle.
If you're going to use a dishwasher, I would limit it to molded cables like power cables or speaker cables, where there are just a few wires, the wires are heavy, you're dealing with low frequencies, and the molded connectors hermetically seal the ends.
Insidious Water
Where you have openings into the connector or cable, water (and detergent), is likely to wick in and will be difficult to remove. Capillary action can pull liquid into nooks and crannies, and into the cable, where evaporation can take ages. Using heat to dry it out may even make it worse because the cable can act like a heat pipe; the evaporated water spreads as a vapor to other areas, so you can end up spreading it more than getting rid of it.
In any kind of cable, residual water can, over time, cause the conductors to become brittle and more prone to breakage (through oxidation and chemical and electro-chemical reactions mentioned in the answers by txtechhelp, Nick T, and Tonny). The thinner the wires in the cable, the less metal they have and the more susceptible they are.
Different Types of Cables
If water gets into low frequency cables, it can shorten the service life of the cable, but it probably won't significantly change the cable's performance. Cables used for high-speed data communication are a different matter; the water, itself, can be an immediate problem because these cables aren't just wires and connectors. Their performance relies on electrical characteristics of the cable design. Water can affect those characteristics and degrade performance.
Cleaning Recommendation
What you're trying to get rid of is external. The cables should still be internally good. If you get water inside, you may create issues you don't currently have. A better solution is to just clean the cables externally by hand by wiping them with a rag and some isopropyl alcohol.
Risks
The risks relate primarily to the performance or service life of the cable. The only risk of damage I can envision to something other than the cable would be getting water inside the plug of a power cord. You could potentially get leakage currents that could corrode the wires or cause other problems beyond the cable, itself.
TL;DR: buy a few bottles of 91% isopropyl alcohol and a small bucket, dump all that in there and scrub the cables in there, then do a sponge bath and wipe with a non-static producing cloth (paper towel for instance).
There's a couple of issues to concern with if you do wash them in the dish washer. First as you've noted, is the heat the coils or water can reach. Most consumer dish washers can operate up to 180 degrees F (for things like the sanitary wash), and usually spray hot water around 130 F. While the water temperature won't do much to the sheathing on the cables (like melt them), you might have issues later.
As an example, HDMI has an operating temp of 80C (176F), so if you did a sanitary rinse on the HDMI, you might change the physical properties of the wires themselves and make them not preform to the spec. If some cables can't operate to spec they won't work at all.
Another issue is in what condition the sheathing of the cables are in. A lot of cable types have a cheaper grade plastic rubber coating that will crack or melt easier than other types, especially under non-ideal conditions (which you're essentially shoving the cables in a thunderstorm in the middle of a desert). There's also the potential the cable might fall through the racks and land on the heating element, and melting completely (I had a lid do that, melting plastic in a dish washer is not a fun smell).
Additionally are the detergents you would put in. Putting anything in your dishwasher that's not a dish detergent might mess up your dishwasher, while putting dishwasher detergent might mess up the cables or connectors (salts + metal + water = no good long term).
Answering your questions
Power cords with AC/DC Transformers attached
Would most certainly fail after being washed. Water plus heat on small IC's can short them out or just completely destroy them.
If there is concern about the temperature of the dishwasher (although I cannot imagine it hurting the cables and not a keyboard), can they be washed by hand?
Yes, you can wash the cables them selves. For the electrical contacts or other small electrical circuits, use isopropyl as it's effective at getting grime and dirt off and doesn't interact with the electrical components (plus it evaporates in minutes for small amounts). If you have a lot of cables that are grimy, you can get a small bucket and fill it with the alcohol and scrub and clean them that way.
If there is any water left in the cables after several weeks of drying out, could they damage the electronics they are plugged into? Or will they simply not function?
If there's any water left in the cables after several weeks of drying out, then chances are there's a small puddle in the cable or you have them in a humidor. Water isn't good for electronics because it conducts electricity and can short out whatever component you have.
As an extreme example of what might happen: water shorts the USB +/- power lines when you plug it into your laptop creating a feedback loop on the bus which would actually cause the bus to blow up (literally pop the IC's).
For reference, I've also put some common operating temps with a few of the cables from your list:
- HDMI cables: 80 C
- SATA cables: 80 C
- Cat 5e/6 ethernet cables: 60 C
- USB cables: 50 C
Sources: my military experience taught me many ways to clean cables covered in sand or other mystery goo (as well as how NOT to clean them).