I have installed tstats that use a small internal relay
whuch is controlled by the the thermostat's control board . The relay provides isolation between the furnace power and the tstat. The relays work well on AC but DC would destroy the relay due to arcing. Other types of tstats use furnace power to maintain the memory and charge the battery
I am not stating that the Honeywell RTHL 111 will not function properly but from my trade experience
I have ran into numerous problems from mis application of products . I worked on a hospital heating control system where some one replaced a 12 VAC relay with a 12 VDC relay . The DC relay did not burn up but due to the lack of a shading coil, the DC
relay chattered .The chattering introduced spikes and destroyed a $4000 boiler control board ( twice)
I am apprehensive about using a product that is rated for AC on a DC circuit due to my experiences.
I am not trying to make this difficult. or argue .