I wanted to pass on some information on how I resolved the sweating toilet. This will probably only work where the washing machine hookup and the toilet are back to back on the wall.
Here is what I did. I took off the washing machine hoses and put a Y on the hot and cold supplys. I reconnected the washing machine H and C hoses.
Now from the free H and C on the Y's, connect a hose to a check valve to a hose. Make sure to use a brass check valve so it can handle the hot water.
When you flush the H from the washing machine supply will feed into the C that feeds the toilet 50/50
My well water is like 45 degrees, with the 50/50 mix it fills the tank at about 75 degrees and NO MORE DRIPPING TANK, NO SOAKED FLOOR.
I have had this hookup for 30 years and ZERO PROBLEMS!