What is wrong if enything about having the boiler thermostat at a temperature under "Yad Soledet bo" and I use the hot (warm) water in the house?
It is permitted to heat up water on Shabbat by setting the thermostat of the boiler below the temperature of “Yad Soledet Bo” [45 C.]. It is not forbidden even though it is causing the heating elements to turn on, because it is secondary Grama and Psik Reishah that is permitted. According to Rav S.Z. Auerbach ZT”L it is preferable to install a timer that will turn on the electricity according to set times, whether the water is cold or hot, and the electricity will only stop if it reaches the set temperature. Nevertheless one should be careful not to use the hot water if the current water that is in the tank is boiling hot [ Temperature of “Yad Soledet Bo”], because he is cooking the cold water that comes in to the tank and mixes with the hot water. It is permitted to use the hot water that was heated in the way stated above, only in order to wash dishes etc. but not to wash himself, even his face, hands and feet. [שש"כ פרק א הערה קיח ופרק יד סעיף ב ובהערה יא, מ"ב סימן שכו ס"ק יז].