After some simple measurements I found the system simply consists of a temperature operated switch. To make the system come on was as simple as setting the desired on temperature, and connecting and disconnecting the thermostat via computer control.
The circuit only switched a 24 V ac line which then switched various mechanical devices which controlled the gas values and safety interlocks. Dad inserted a SSR in series with the circuit which was then wired back to our computer controller.
The system has been running reliably - and has a few hidden benefits: We can keep our 'perfect' temperature, as the position on the thermostat doesn't change; the heating is never accidently left on - as the computer turns it off at midnight and lunch time whatever settings are used.