I have a bathroom in the hallway which is now the warmest room in the house (after the master bath was torn out). The tiles on the floor still feel cold (the room underneath is heated). So a warm room itself does not make the tiles warm. Well, the tiles will be warm, to the room temperature. But tiles are good heat conductors, so when warmer feet are on them, they take away the warmth from the feet. My old master bath was an exception, because right underneath its floor there were 3 big heat supply trunks taking off the furnace, and all the supply ducts are over 90 degrees hot (I measured with an IR method) Those supply trunks were the heat source for the floor tiles.
In your case, mediaman, my guess is that there are not too many heat supply ducts under your bathroom floor, because your furnace is 2 stories down. The floor will be heated but no higher than your thermostat's setting. I don't know whether that's comfortable enough for you. I just know that with all the material at the same temperature, carpet will feel the warmest, followed by vinyl, then wood, and tile will feel the coldest. It's determined by their heat conductivity.
You probably will be fine with mats. And if you wear socks or slippers you won't feel cold on tiles anyway. As for resale, heated floor is something the buyers would love to have but not willing to pay extra, and it's not something that makes or kills a deal. I wanted it just because I was spoiled by the "free" one (no installation nor operating cost).
If you have all the dimensions marked, you might be able to use your drawing with your contractor. Or you can give them your sketch and description and ask them to make a formal drawing. My contractor actually used my drawing for their permit application, no formal architectural drawings needed. But your current sketch is not sufficient. You need to provide spec for everything - you need a measurement for every single line in your drawing, and 3D specs too (how tall the cabinets are, how tall the mirrors are, how tall the tub deck is, etc). The accuracy of your requirement should be within 1", but don't expect the builder can follow that exactly. Given that the existing corners may not be square, walls may not be parallel, you'd better prepare for 2" margin. Anything that needs to be more accurate you need to have that requirement on paper. Say you want to use a stock sized shower door so the wall next to it should be build accordingly. I'd suggest to ask the shower door manufacturer about the opening requirement, and discuss with your builder.
One thing I learned after hefty "tuition", is that on your contract all the requirement should be in your own words, or in words/terms you fully understand. Otherwise you nay not be able to use the contract to protect you. I had a window company to measure an existing window and told them to add one of the same size to my new bathroom. They wrote down the measurement of the new window in the contract and I signed it. It turned out their measurement was wrong. I had to buy another window and they would not refund me money for the wrong one, because they ordered what was on the contract. You see, if only I insisted to write down "same size as the existing window" instead of just their measurement on the contract, I would stand a good chance getting my money back.
There is a saying, "trust, but verify". I think it's perfect for dealing with contractors. Then at least you need to know who is trustworthy and how to verify.