Weather dependent thermostat

Hello.
HA have all components for make this thermostat.
I think prediction need make from two sensors: weather forecast sensor and external temp sensor.

Sorry but what are you suggesting ?
External weather does not affect what temperature you find comfortable.
Not many boilers have controls to allow remote adjustment of water temperature (to heat your room faster) just on-off
Set the water temperature higher and you lose the efficiency from the condensation phase change
Alternative is to start heating earlier.
How much earlier depends on your house, room sizes, numbers of radiators, volume of system, efficiency of system and if you are constrained by burning radiators (children).
Just set your system to come on 15 mins earlier if you are chilly getting up.
If you’ve been out all day then set triggers for when you leave certain locations with timers if you need to. Adjust those timers as necessary, build a pattern then do it.