Cold start furnace w solar hot water tank

ted_52_tops

I have a smith boiler, basic for houses. It had a standard controller on it with a high and low cutoff, so when heating baseboards in the winter it would run to the high, cutoff and circulate and stay off until the boiler reaches the low then it would do a nice long fire again to bring it back k up to the high limit. When the solar hot water was installed, the wiring was done so the hot water tank would ask the boiler for hot water, in the event it got cold inside the solar tank, like Dec-feb. it was converted to a cold start. This works ok for the potable hot water in the solar tank, but now in the winter when the furnace is used to heat the baseboards, it turns on when the thermostats upstairs ask for baseboard heat, but it does not seem to have a high snd a low. It fires, heats up, shuts off, then in about 5 minutes has to fire again each time it needs to circulate hot water. I want it to start when the thermostats ask for heat, run to the high cutoff, then stay off until it gets to the low cutofff, like range of 120-190.  Is there a terminology I can use to try to get a heating installer to put in a new controller that will let my solar tank ask for hot water but also let it work correctly for the baseboard heat? There is a controller on the solar tank, a new controller on top of the furnace thrn these wire into the original controller on my furnace that was converted to a cold start. Help!