Just yesterday I was talking to a sales representative for Nest and he shared with me he installs his own thermostats, smoke/co detectors, and drop cams in places that he rents.

She put locked covers over their thermostats so that they can't turn it too high without her permission. 

I don't do anything else with the utilities except change the thermostat temp. 

....Let's just say, they've already called in enough service calls for problems that literally equated to changing the battery in the thermostat.....

With a forced air gas furnace, you typically have one central thermostat to control the whole system.  

Another solution, is to stick with the same configuration but couple a high efficiency replacement with programmable thermostats.

(depending on your market)Try to avoid an over under situation if possible, unless newer with sound deadening between the units,  i have  owned many of these and renters always complain if they hear the tenant above or below.Separate utility metering and thermostats eliminates a lot of tenant complaints also.

The building was occupied by the owner who lived in one of the units and had the thermostat that controlled the heat for the entire building in her unit.The heat for the building is produced by a single gas fired steam boiler which was installed last year when the old oil boiler was replaced.What is the best option for controlling the heat for the property?

I did have one tenant get frustrated with us because we locked the thermostat (put a cap on how low/high he could adjust the temp).

We have thermostatically controlled faucets in our bathrooms.