There could be a lot of different things at play here. First, many modern thermostats are "adaptive" in that they try and learn how long it takes to get up to the temp setpoint, and many do this by sensing the temperature of the wall upon which they are mounted. Sometimes this adaptive feature can be turned on or off; for example let's say you don't CARE what the temperature is at 6AM in the house, but THAT is the time you want the boiler on, then you want to disable adaptive feature if you can. Others say, "I want the temperature in the house to be AT 70 degrees at 6AM" in which case some intelligence is used in the adaptive feature.
On my hot air system, I used to have simple Honeywell digital setback thermostats. One of the things they did, as part of the adaptive feature, is they used to call for heat in the middle of the night when you didn't expect it. I had the night setback to 62 degrees, and the morning temp to 72...but the stat must have thought that spread too great. So, while it kept the night time temp to 62, the heat would often come on briefly bumping the temp up to say, 64 or 65, beyond the setpoint...and I think the purpose there was to prevent an extraordinarily long anticipation time before the official 6AM call for heat. It did this during periods of extreme cold or when I had that setback to 62. After a call to Honeywell, their support folks said don't set back more than 5-6 degrees for "optimal" use.
Don't forget the concept of "thermal mass"; that is, you can heat the air in your room(s) to the comfort level you want, say 70 degrees, from 60 degrees, but for the first time it hits that setpoint, the room will not be comfortable because only the air at the stat has reached that temperature. It takes a LOT longer for everything IN the room (including walls, floors, etc.) to absorb the heat; and only when they do will you have a comfortable environment.
The location of the thermostat as well as the location of the heat sources (vents in a hot air system, or radiators in a hot water system) make a HUGE difference. Say you have the thermostat in an upstairs hallway, but everyone sleeps with the bedroom doors closed. Guess what? The heat will NEVER get to the thermostat setpoint! You have it set for 70, and it may get to 75 before someone wakes up in a sweat, opens the bedroom door, and finds the bedroom hot and the hallway cold. Hallway locations for thermostats in living area are a bad idea if doors are closed, doors to rooms that have the radiators or ductwork in them...and yet, in a two story home, the pros will ALWAYS put the stat in the hallway. I had to insist that it be put in my master bedroom just to prevent the scenario (which I experienced once) from happening.
There is also some intelligence and adaptive technologies built into some furnaces and I'd imagine, some boiler controls. One of them is the old school "anticipator" which is a mechanical device. They are generally on the boiler control and used with older mercury style thermostats. If your boiler has an anticpator, and you have a modern digital thermostat, unless either the adaptive feature is disabled on the Tstat, or the anticipator on the boiler control is bypassed you can have these smart features fighting each other.
Best to contact the boiler installer/manufacturer and find out what you have, and how best to install a modern thermostat. Digital stats with energy saving setback features (to turn off and on the heat to different setpoints) are pretty cheap these days. Ones with Wifi or internet control are a bit more costly, and then of course you can break the bank and get a Nest...