There's an example here. but it would need to be mounted in an enclosure.
The fan timer link that I posted earlier, see here, does the same thing but comes with an enclosure.
The timer is also controlling the boiler. So, if you were also connect a permanent live to 'C' it will also be connected to the boiler and keep it 'on' permanently. The thermostat could be wired to make use of its changeover contact to avoid this as below.
View attachment 140046
1. When the pipe is cool (the position shown in the diagram above) and the timer switches on the boiler, the pump will also start as the thermostat connects it to same switched live from the timer.
2. As the pipe heats up, the pipe thermostat contact will switch over, and the pump will now be connected to the permanent live.
3. The timer goes 'off' as does the boiler, but the pump will continue to run from the permanent live.
4. The pipe cools and the thermostat switches over back to the timeswitch live which is now 'off' and the pump stops.
Stem/heat service - this makes sense ... do you have link to a specific pipe stat model I can look at to follow up this connection? thanks