It could be trapped air simply blocking the pipes and moving about causing the intermittent heating that you describe.
With the heating on, try shutting entirely all the radiators that are getting hot. This may force the blockage into the radiator where it can be bled off.
I assume open vented: The hot water flow circuit needs a valve to restrict flow through it. When the hot water circuit comes on and there is no restriction, the water simply goes the easiest way - 80% through the hot water circuit leaving 20% for all rads.
The other option is pieces of sludge or debris in the pipes moving around under different flow conditions. If your water is black - power flush the whole system. Draining it down will not be enough.
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