I wash up in cold water although I would wash everything more carefully as you haven't got the assistance of hot water killing germs. many people in countries without hot water wash this way and lets not forget its using less energy! :)

hot water kills germs.

use it to wash you dishes.

My anecdotal evidence suggests the hot water definitely helps as it does "melt" the grease. Take a frying pan that's covered in grease and put detergent into it and start scrubbing – it will make a grease/detergent combo. Take the same pan and pour boiling water into it and watch it melt, add detergent and it disappears really quickly. Hot water from the tap would suffice as well. 

Scientifically I have no proof but certainly in my experience it definitely makes a difference!

Washing dishes in water hot enough to kill most bacteria would be intolerable to touch.  Suggested safe hot water heater temperatures is around 125 degrees F.  Our autoclaves used to sterilize biohazard waste normally cycle at 250 degrees F and 15 psi for 30 minutes at least.  So your tap water at its hottest isn't going to kill bacteria.  Warm water will facillitate removal of fats and oils by melting them and allowing them to be dissolved and pulled away more easily by the soap or detergent.

Although many people will probably say that hot water is necessary in order to kill bacteria, in reality most people do their washing up at a temperature far short of that required to have a sterilising effect on your cutlery and crockery.

According to the US Consumer Product Safety Commission, a temperature of just 48° C is sufficient to scald the majority of adults after a few minutes' exposure - so one could reasonably infer that even when wearing rubber gloves, most people won't have their dishwater much hotter than this.

In contrast, most wet-heat autoclaves require a temperature well above boiling point to be held for a sustained period, typically over 15-20 minutes, in order for MOST bacteria to be killed. You can see therefore that, for sterilisation purposes alone, there is practically no difference between using 'hot' water (which is really just warm) and cold water.

With fats and grease, however, it's a different story. Washing up liquid will indeed do its job at low temperatures, by using a cocktail of different ingredients to achieve a variety of effects - surfactants in particular reduce the surface tension of the water, allowing easier lifting and dispersal of dirt and stains.

However, as with any process involving chemical reactions and the breakdown of molecules, a higher temperature will significantly affect the rate at which the dishes can be cleaned. By turning up the heat, you impart a great deal more energy to the active ingredients in the detergent, which allows them to bombard their targets with much more gusto.

Aside from that, of course, by washing up in warm water you're also raising the temperature of any fat left on the dishes. Those naturally liquid near room temperature will decrease in viscosity, and most solid fats (such as cooled beef dripping) will simply melt away and disperse in the water.

So in summary it's a matter of choice - if you only wash up in cold water, then it really just depends on how much more quickly you could finish the washing up if the water were hot. If it's one or two items you might as well give them a quick scrub under the cold tub, but cleaning up the mess after a Christmas dinner for 10 people will undoubtedly be easier if you wait a few more seconds for the hot tap to run through!