Way to cold for coal or any fuel for that matter.
What your doing is very dangerous and will eventually cause severe property damage or someones severe injury or death.
Limiting the burn times and rates by short cycling the fire is going to create massive stack condensation and coal tar formation. Basically your building your own death machine out of your boiler.
Once coal tar builds up to a thick enough level and gets hot enough it will spontaneously ignite and then it burns hot enough to melt stainless steel chimney liners and shatter chimney brick material. Then the house and everything and everyone in it goes next.
Short cycling a coal fire like that to maintain a low stack temp creates high levels of coal gasification and carbon monoxide as well plus makes for extremal inefficient use of your coal.
Most of your coal never gets burned in the boiler to make heat but is instead uncontrollably gasified into crude but highly explosive natural gas and highly flammable coal tars. Its a bomb and a unstoppable stack fire waiting to happen.
I am not sure where you came up with this idea but its very poorly thought out and will never work as your hoping. Please consult a licensed and certified boiler technician or service engineer and have him rework your system to work as the manufacture intended for it to. Or at least read and understand your manual.
If parts are no longer available and what you have is a home made hack job please get rid of it or get some solid education on how boilers work. If you dont your going to get yourself or someone killed eventually if your house doesn't burn down or blow up before then.
If your doing this to save money please contact your insurance company and tell them what you are doing. They then will happily cancel all of your homeowners and life insurance policies which will have you far more money that way.
Sorry but you really need to know this before going any further with your design.