I disagree. Most tankless heaters do have a thermostat. My water temperature coming in is now 40 degrees, and my older 125,000 BTU tankless has no problem at all delivering 125 degree hot water to the last fixture.
Crunching the numbers, it looks like you can heat ~2.2 gal/min with a 85 F temperature rise. So your right at the edge of your capacity. But, overall I think this would be a good application for tankless WH.