The heating effect of the water bottle depends on two factors: the relative temperature difference between the contents of the bottle and the bed, and the total mass of water. As long as the bottle is warmer than the surroundings heat will flow from the bottle and warm you up. The total heat available to warm you (as measured in calories) is the product of the (water temperature-room temperature) x mass of water. If you add more room temperature water, the number remains constant. You can think of it in terms of money. If you have a room with 100 people, each with $100, and 100 broke people enter, the total cash in the room is not changed even though the per capita amount has dropped.

The rate at which the heat transfers depends on the difference in temperature between the bottle and the bed. If you have a very hot small bottle you will get a fast but short-lived warming. A larger, cooler, bottle will not have as great an initial effect, but will last longer.

Yes, but to put a slightly different emphasis on it, you will get less heat from the bottle with the extra cold water. Such heat as you do get will last longer, as Mike described, and as such it would be more useful to you, but arithmetically it still would be less, because at the point at which the water had reached the temperature of whatever you were warming, there would be water that had been cold and now is slightly warm without warming you.

If this offends your sense of economy, as it does mine, then rather use alternative means of slowing the outflow of heat. For instance, try wrapping the bottle in a towel, or even a pillow slip. That works well at any temperature that the bottle can safely survive.

The simple answer to your question is yes, adding the room temp water does reduce the amount of heat delivered over night. Here is why.

There are three important temperatures, the temperature of the hot water, the temperature of the room temperature water and the final temperature of the water in the bottle.

If you do not top the bottle up with colder water, the water in the bottle will continue to deliver heat until the temperature of that water has fallen to the temperature in your bed, I assume that this is above room temperature.

Now, if you do top up the bottle, all of the water in the bottle ends up at the temperature in the bed. This means that the original hot water has cooled but the room temperature water has warmed up. The only source of heat to warm the room temperature water, if we ignore your cold feet, is the original hot water. This means that there is slightly less energy available to heat your bed.

I read a tip recently (might have been The Last Word books or a newspaper, but I can't find it now): mountaineer claims if you stand in snow barefoot before getting in your sleeping bag, you will be warm all over for the next eight hours, including those feet.

The reason is that your body has a wild and persistent over-reaction to the sudden cold. So, conversely, warming your feet probably absolves your body from taking care of them, and may chill you all over also.

In the absence of snow, try immersion in cold water for a couple of minutes, and wait for the glow.