Here's a scenario I was faced with recently. We do a climb that involves going up to a mountain hut and sleeping there the night before summit day. There is no snow at the hut to melt for drinking water, so we have to carry up all our drinking water. This is in Mexico (on Iztaccihuatl), so we're buying water in bottles. Temperatures at the hut are forecast to be below freezing. On the night before summit day, we can sleep with water bottles inside our sleeping bags to keep them from freezing. But on summit day, we need to leave most of our water at the hut, to which we'll return. Although we can leave these bottles inside sleeping bags and hope they won't freeze, we can't count on that, so the expectation is that when we get back to the hut, all of our water is frozen.
In this type of situation, what good techniques are there for getting the water unfrozen?
The best plan I was able to come up with was the following. Bring up a plastic bucket. Before heading up on summit day, remember to pour out some water into a pan, and more into the bucket. When we get back to the hut, melt the frozen water in the pan, then use an ice ax to chop more ice out of the bucket and melt that as well. (A variation on this plan would have been to not use a bucket, but use hot water in the pan to thaw out the frozen water bottles, by dunking the water bottles in the hot water. I think this might have been much too slow, however.)
I didn't actually get a chance to try this plan, because conditions changed. (A big storm came in, and dropped a lot of snow at the hut, but the storm also prevented us from doing the climb.)
[EDIT] Some of the answers and comments have talked about using big pots, building campfires, and hanging things from above. My question is about mountaineering, so none of that is applicable. We're above tree line, and the heat source is a stove. Although in this particular situation we might have been able to hang things from above (because we were going to be in a mountain hut), that would not be possible in general.