At a previous House the boiler (Trianco) had no weather compensation but worked very well with the Honeywell AQ6000 Weather Compensated Control System (now discontinued)
The AQ6000 had three temperature: external, internal and water flow temp. It used the information to determine how long the boiler ran for. It did not directly control the burner or the gas flow, just turning the boiler on and off for varying lengths of time.
I am guessing now, but it would seem to work like this: If the house was cold, it would run continuously to bring the house up to temperature. When nearing the required temperature, it would shut the boiler down for a short while, to let the accumulated heat from the rads dissipate, then start up again. The boiler would then cycle on and off with the % time on and % time off varied according to the data from the sensors to keep the house at the required temperature.
However, I was of the opinion that a Weather Compensating Heating Controller did all the work and fired the boiler as required.
All the weather compensator does is to adjust the flow temperature of the boiler so it is no hotter than is required. See
Flow temperatures in heating systems
With this in mind, it would be no different to running the boiler from a single channel Horstmann timeclock or Alpha's plugin Timeclock. Using a controller with Weather compensation would still switch the boiler on and off but with the advantages of weather compensation.
But the basic time clock just turns the boiler on at a set time.
Say you want to get up at 0730, so you set the time switch to 0630. At 0630, the time switch turns the boiler on and it runs to bring the house back up to 21°C. If it has been a very cold night it may take one hour to do this, if a warm night only 15 minutes. This means sometimes the house is up to temperature too early, sometime just in time and sometimes it has not reached temperature when you do get up. Weather compensation does nothing to correct this problem; you need a programmer with optimum start features, such as the Honeywell CM900 series.
This learns, over a few days, how long is needed to heat the house up to the required temperature and then adjusts the turn on time so the house is up to the required temperature. You set the required temperature and when it has to be up to temp on the programmer. The rest is up to the programmer. One word of warning, these programmers have an optional outside temperature sensor. It is
not a weather compensator; it just allows the outside temperature to be displayed on the screen.
The temperature control facility of the AQ6000 is provided in the CM900 by a P and I controller, which varies the % time on and off, so the house heats up quickly, and then maintains the temperature within 0.5°C.
I have had one of these for over two years and it is very good.