Rabbi,
Is it permitted to use hot water on Shabbat if you lower your boiler setting below a temperature of yad soledet bo? If so, would there be a concern that even if you did lower the setting the boiler would refill with cold water which would then mix with the hot water already stored in the boiler from beforehand?
thank you
Akiba Gali 
Danielle Prizament 
fito Jamous