Honeywell 4006a aquastat

I have a hot water system which was converted from oil to gas many years ago. It also had a tankless heater which was replaced by a Rheem Natural gas unit.
My question is this. The furance still tries to warm the water up even though the thermostats are set low. Like it's trying to maintain the low temperature.
My understanding is that the gas unit for heating purposes should only kick on when the thermostat triggers the circulator pumps to circulate the hot water.
I just turned on the main switch today and when I did that the burner (gas) kicked on. Even with the thermostats set low.
I know I'm going to get hammered this year with natural gas prices going up and I'm just trying to conserve cash.
Thanks, Chuck.

if you can find the schematics, you could jumper (or open depending on NO or NC for that function) the thermostat for the hot water section so thatit would think the temp was adequate. Then, it should only turn on if the room thermostat called for space heating.

Aquastat

The boiler can be wired either of two ways depending on the controllers. Either the boiler can maintain a set temperature and the thermostats will turn the pumps on and off, or the thermostats can operate the pumps and the burner as necessary. This requires a more sophisticated control system which you may not have. In the first case the burner will operate when the system is turned on.