Our bathroom had an optional double sink in the main bathroom from when the house was built (before we lived in it). Based off of water temp alone I'm guessing that the toilet & sink are on the same set of lines. Water pressure doesn't change when the toilet is flushed but the sink does get significantly warmer while the toilet tank is refilling. I'd like to convert the single to a double sink. My question is what sized lines are needed to make sure that everything has the needed pressure? This is a newer construction house (early 2000's) with pretty good water pressure throughout.
As country handyman says, if the're already supplying enough you don't need to change them.
However, if you're seeing a temp increase when you flush, then you ARE losing pressure, and the hot is making up for it, unbalancing your temperature.
I'll wager a guess that the pipe is currently 1/4 inch and that the toilet is fed before the sink. If that's the case, then when the toilet is running there is less water flow available to the sink and/or shower (assuming it's on the same line too).
So if you're opening up the bathroom walls anyway, you can do two things here to deal with this:
Reroute the cold so that it goes to the sink first and then the toilet. (Or better, shower, then sink, then toilet)
Increase your pipe diameter to the bathroom and split off 1/4 inch lines for each fixture.
In my own case when I remodeled, I replaced the 1/4" galvanized line to the bathroom with 1/2" PEX, and used 1/2 : 1/4 T junctions to split off feeds for the toilet and sink in that order, then reduced the line to 1/4 for the bath/shower.
Now we can run the sink and flush and the shower temp/pressure doesn't change, BUT we also put in a temperature regulating fixture, so... YMMV
You don't need to change the pipe size, If the size pipes you have already are supplying enough pressure.