I wasn’t able to locate the source for the idea that if one sets the thermostat on his water heater (boiler) below yad soledes bo, then it is permissible to use that water (even if the boiler is not operated by timer) because any heating caused by opening the faucet is just secondary grama and psik reisha. Can you please quote the precise source? Thank you very much.

Sefer Shemirat Shabbat Kehilchatah Chapter 1, note 118. Chapter 26 note 31. From Responsa Har Tzvi Orach Chaim 133 & Responsa Avnei Nezer Orach Chaim 194 (2).