My installer completed installing our 3/4 inch 4 inch wide rift and quartered red oak floor. I noticed that on one wall, the wood is pretty much right up to the sheetrock. This is one of the 4 inch wide sides not the length of the board side. I did not put the molding back up yet and I am now concerned that there is not enough room for expansion. The room is cold in the winter and I will likely install radiant heat in the joists below. The floor is already finished. He has to come back to clean up some finishing touches. But, when I went to put the molding up, I noticed how close the wood is to the sheetrock. There should be additional room on this one side correct? The 3 other sides have space. Thanks.

Generally, yes. If you want an expansion gap use an oscillating multi tool with a plunge blade to remove the sheetrock. Lay a thin piece of plywood or Masonite or linoleum, etc on the hardwood to protect it from the tool and just run the oscillating tool along the wall. A shop vac will help with the dust. The baseboard will cover the cut line. If you don't have one of these tools you can get one at Harbor Freight for less than $20. A cheap blade will be fine for sheetrock.
Just out of curiosity I would ask the installer why he didn't leave an expansion gap on this wall but left them on the ends of the rows which isn't really necessary.
Also, you're aware that hardwood floors are happiest when humidity levels are controlled year round?

I do plan to control the humidity. We live in NY and we will be running a/c in the warmer months. However, this room is over a garage and gets cold in winter. Radiant heat is going under in between the joists. We had chosen rift and quartered for the look and the added stability. He did a beautiful job upstairs through the rest of the house. But, his guy who installed the floor ran it up to the sheetrock on one side.
For my own knowledge, you don't need to leave a gap on the long edge side of the board?
Also, couldn't I have him cut the wood along the wall? I rather not mess with the rock. It took me a long time to get the walls nearly perfect. Can a fein tool or other saw cut the wood and leave the rock alone? Thanks so much for your help.

Yes, the wood can be cut but be careful so the cut edge will be covered by the baseboard. The sheetrock cut off at floor level will be covered by the baseboard. I regularly cut the bottom of the sheet rock before putting flooring down to leave the expansion gap.....did it by laying a piece of the flooring on the subfloor and resting the oscillating multi tool on it and running it along the wall.....fairly quick process.
Check the flooring manufacturer's installation instructions and ask the installer why he didn't adhere to them.....out of curiosity of course.
One more thing (just to be anal). If you cut the sheetrock (1/2" ? thick) and then install the baseboard (1/2" ? thick) you will have a 3/4" expansion gap. If you cut the flooring and have a 1/2" baseboard the expansion gap will be less than 1/2".

Ok, thank you. He is coming Tuesday morning. I don't fully understand the gap difference between cutting wood vs sheetrock. If we remove the 1/2 inch of rock vs 1/2 inch of wood. But, I do see where cutting the rock will be faster and eliminate risk of overcutting wood, which would be an epic failure.

No difference.....you're just leaving a space that the hardwood can expand into if it picks up a lot of moisture. If the hardwood is tight against pipes or even wall framing and the hardwood wants to expand it could damage the pipes or even move a wall. I'm assuming regular baseboard, the top of which will be well above the cut line and totally hide the removed sheet rock.

Flooring guy does not think I need to cut the 4 inch wide ends of the wood. He believes the expansion will be from the length side of the wood because that is the way the grains run. ?? It is rift and quartered sawn wood red oak.

These boards will be more dimensionally stable than flat sawn. Check the manufacturer's installation instructions concerning expansion gaps.