The problem
The picture shows a typical hotwater/heating system for a third floor unit. It is my understanding that the second floor systems are different but utilize the same mixing system. There is no separation of the floor and domestic water. Water that passes through the mixing valve goes to the domestic hot water and to the floor manifold.
At the height of our problem, the heating thermostat was turned off. The hot water tank was set to full hot and the pipe coming out of the tank measured 160° on the surface. Domestic hot water from the tank was 100° measured at the tap.
The outgoing manifold was warm to the touch and there was warmth in the floor even though the thermostat was set to off.
While most hydronic heating systems separate the domestic and heating water, this oned does not. In this situation the natural draw of hot water at the tap will cause some draw through the floor. Hence, even in summer the floor is being heated.
We discovered the mixing valve adjustment did not function properly. It was set to the maximum of hot water but mixed down to about 100°. When adjusted in the past by turning it full open and then back to full closed it would produce very hot water at the tap. Then it reverted back to the lower temp. Eventually it quit responding to any adjustment.
The culprit
This is the 
mixing valve. It had failed. The solution was to replace the valve.
We had this work done by Janes InFloor. (Telephone: 425.267.0202) They are the contractors that did the original installation in the building.
We were not entirely satisfied with their service. It took two visits from their tech person to figure out the problem. That was because the first person really had no understanding of the system. The second person understood the system and recognized the source of the problem immediately.
Also, Janes was a bit expensive. The work, including the two visits and the new valve was over $500.
I know at least one other unit has had the same problem and they used a regular plumber who provided the part and labor for much less. Maybe that person will post a comment that will provide more information.
Please feel free to call me at 206.418.6331 if you have any questions.
Jerry Taylor, Unit 303
Dixie Buol comments:
I experienced the same problem with the mixer valve on my heating system. The plumber who replaced the mixer valve was Scott of Simjple Solutions. My total bill with tax was just under $500.00. His phone number is 206 355-6296.