Apparently, Octavia heater problems are super common, and super common on the VW Golf MK4 GTI platform in general. The issue is caused by the blend doors.
VW in their wisdom decided to use blend doors which have holes. And they decided to fill these holes with foam. And shock horror, this foam slowly degrades over time until there is no foam left. Which makes the blend doors useless.
The solution is to plug the holes in the doors to restore the heat. Unfortunately, the entails disassembling the centre of the dash and the plastics between the seats. This is how I fixed the heater not working in the project Octavia RS (MK1).