I am not very educated at this process yet, so my comment is just my opinion from what I have read so far. Moving the cheese pot around during the process is not good because you do not want to disturb the curds during formation. Once the curd is set and you cut, you can of course move the pot because you will be stirring the curds from time to time.
A double boiler or a smaller pot inside of a larger one will allow you to heat the water in the larger pot to maintain the temperature in the smaller one. The smaller pot should not come in contact with the bottom of the larger pot because it will pick up heat from the heat source.
Or you can just add some hot water to your sink - this is the easiest way but not necessarily the best way to do it.