For the most part I agree with everyone so far, though Tom gives the most impressive summary.

I have just two points that I wish to re-emphasise, rather than "correct" anyone.

Firstly, I think that the effect of heat on solid lipids is somewhat undervalued. Hard, waxy tallow-like fats will certainly leave more residues in cold water (especially positively chilly water) than in warm water. There are several reasons. Firstly, if they are liquid, then in the presence of detergent and  turbulence, they wash away very effectively. Secondly, the detergent effect partly depends on the ability of molecules to diffuse into position between the lipid molecules. Not only do they diffuse more rapidly at high temperatures, but they can diffuse into the surfaces of liquid lipids more effectively as well as more quickly. In fact they are pretty nearly useless against lumps of fat unless you are willing to do a lot of extra scrubbing. In summary, if you can afford the luxury of hot water, use it.

It is all very well speaking of the economy of using cold water, but it entails the diseconomy, not only of extra effort, but of extra detergent to achieve even nearly the same effect.

Some of the correspondence so far have correctly pointed out that you might as well hope to grow wings as to sterilise your washing by using hot water. However, I think they overemphasised the point in context. Water at temperatures approaching 50°C (which is close to scalding; I mentioned it in the context of jellyfish stings not long ago) actually will kill most everyday microbes in their active form (as opposed to say, spores). This is not to say that it will kill all the microbes that are not in spore form, but it certainly will reduce the count of living microbes, including many pathogens and spoilage microbes. This might not be good enough for hospitals and places of commercial preparation of food, but it could do a good deal for everyday, commonsense domestic hygiene.

In sum, you probably will be doing yourself as well as your father a favour, whether you are lazy or not, by using water as hot as you comfortably can manage without hurting yourself.

As far as the safety issue: it is the washing liquid that is most important. Most contain an ionic detergent that destroys the bacterial cell membrane and kills them: while higher temperatures may speed this up, room temperature is fine.

I agree with you.  Try it.  It takes a little longer cold, but the end result is the same.  Soap and detergent both have molecules which look polar at one end and non-polar at the other, and so render grease soluble in water, even when cold.  When camping I usually wash up in cold and in warm weather I shower and bath in cold water, using soap.

I can't help but feel that those who are stating that the heat involved in washing dishes will not have an effect on bacteria growth are over-stating the relevance of autoclave temperatures.  Yes 121oC for 15 min is needed to "sterilise" an item, but this high temperature is only needed to kill resistant spores, most bacteria cells are killed by about 70oC (as in the pasteurisation process), and are significantly inhibited well below this temperature (one reason why our bodies act to raise temperature in response to infection), so I think it's not entirely accurate to say that a temp of 40-50oC would have no effect on bacteria, it should have a significant reduction in growth rates and viable cell count.

That being said the detergent will have a greater effect in it's own right regardless of temp, the main use of warmer water I would agree is simply to help in the dispersal and emulsification of fats which solidify at room temperature.