Continuing the discussion from Is an oversized Daikin really a problem?:
I don’t know of heatpumps that provide an external signal, but maybe they exist?
If you’re able to monitor flow temperature, either directly from the pipe or by interrogating the heatpump, you can use this to switch on device while the heating is running. There are a number of solutions available, depending on what you already have and how technical you want to get.
I use a temperature sensor relay for one set of fans using an off-the-shelf device, and for another set of fans I use a smart plug controlled from a python script.
More ideas in this topic: DIY Controller for radiator fans