We have hot water heating (radiators) in our house. If they are the old cast iron radiators, they are slow to heat up but when they do, they hold the heat for a long time. That's the beauty of them, actually.
Insulation will not work, period. No matter how good the insulation, the temperature outside the insulation will eventually rise to the average temperature of the radiator. The insulation only delays the time.
You may need to get a plumber to install a cutoff valve in line with the radiator, maybe in the basement. I did that because the valve on the actual radiator (100 yrs old) was stuck open. This might not be what you want to hear, but it is the truth.
Is this your situation ?