"Heat from which a hand shies away" – that is the way the sages defined the temperature above which a liquid is considered as being cooked (Shabbat 40b). This means that one who heats up water (or any other liquid) to such a temperature that a person will instinctively withdraw his hand from it has violated the prohibition of "cooking" on Shabbat. Since not everybody reacts the same way, the sages defined this as a temperature which will cause the skin of a baby's stomach to be burned.
The rabbis of our times have tried to translate this definition into modern day temperatures, and various estimates have been made (ranging from 40 to 52 degrees C). The most commonly accepted opinion is based on a ruling by Rabbi S.Z. Auerbach, which sets this temperature as above 45 degrees.
In practice, in equipment designed by The Zomet Institute where it is desired to avoid "cooking" a liquid (for example, an electric boiler) a safety band of 5 degrees is used. In other words, the liquid is kept at a temperature of 40 degrees or less.
On the other hand, when we are interested in having the water remain "cooked" and not cooled down, so that it can be mixed with boiling water (such as in the gauge of a hot water urn), the temperature is maintained at a minimum of 50 degrees (in the case of an urn, it should be noted that there is no specific desire to mix the water in the main tank and that in the level gauge – see pesik raishai – an inevitable result).