Why does my heating work poorly in moderately cold temperatures?
Just a guess, but the colder it gets the longer the boiler cycles and the hotter the delivery water temperature gets so therefore the radiators get hotter before the thermostat shuts the boiler off.

In moderate temperatures, the thermostat shuts the boiler off before it gets very warm and so your radiators are barely above room temperature.

Check to see if your boiler has any kind of temperature control on the delivery water going out into the system. You may be able to adjust that for better performance in moderate weather.

Good luck with your project!