So I could do work on the boiler to make sure it's as efficient as possible, make sure all the radiators are functioning, and make sure the thermostat is always set to a reasonable temperature. 

They had pipes burst in the winter two years ago, so they were especially keen to install the temperature sensors and water sensors (in addition to all the standard entry sensors, motion sensors, etc.)  

This is all we have re: utilities:Tenant agrees to keep the Premises heated to a minimum temperature of 55*F during cold weather by using the heating equipment on or at the Premises and not by using the stove, other appliances, or kerosene space heaters.

The second and third floor share utilities, with the second floor covering utilities for the third floor, and the tenants agreeing upon the set temperatures, etc.The appraisal came back and said the appraised amount is contingent upon "proof that the third floor has all proper permits (building, electrical, and plumbing)."

The units arent temperature controlled so no worries for malfunctions there.

I am trying to figure out what an acceptable temperature for hot water to pour out of the faucet or shower. 

We've already had temperatures below your average January low (26F, -3C) for Kansas City ;-)

One unit is refusing to keep a schedule in the thermostat, thus leaving air conditioning on 1 temperature all the time.

I can understand if it's a nice high 60s or '70s day and you want to bring in some fresh air, but they often do it when it is more extreme temperatures with complete disregard that the climate system is running.

@Bill Bockwoldt , was nice talking to you again, and thanks for the tip on the attic fan for temperature difference issues.