This is probably a long shot, but do the symptoms below make it obvious to anyone what's wrong with my HEVAC (MY2000 4.0 P38).

After 20 seconds to 5 minutes of driving, the book error comes on.
Temp control for drivers side changes number, but has no impact on the temp coming out of the drivers vents.
If I leave it on a cold temperature however, when I restart the car, I get cold air.
But then the book comes on and I'm stuck with cold air.
Same if I leave it on a hot setting.

I know without a Nanocom or similar, there's a whole bunch of things it could be, but does anybody reading this think it's clear what the issue is?

I have changed a few of the temperature sensors on the coolant pipe coming into the heater matrix, underneath the dash. From what I remember there no longer available but you can fit a standard thermistor on there to give a reasonable temperature measurement.
Are the flaps moving ok ?
Pity there’s no one local with a nanocom.

Most likely one of the three actuators. They are notoriously unreliable, although having dismantled a few, I don't know why.

Also a total pain to change.

Chris. L405 - 4.4SDV8 Vogue
P38 - 4.6V8 HSE
Land Rover series IIA V8

Agreed, it’s likely the blend motors.

I removed the entire dashboard and heating box, thoroughly tested and replaced all the blend motor and rebuilt the box. However, the book symbol still appears, which is probably because there’s no refrigerant in the system rather than an issue with the blend motors.

You can find replacement blend motors online, either used or by searching for Valeo Peugeot 405 blend motors, as they were also shared with the P38.

I didn't use any kind of code reader.

Heating/ventilation works great now! 2012 4.4 TDV8 Westminster - Baltic Blue, Jet interior
1997 P38 2.5 DSE auto & 1998 P38 2.5 DT Manual
1988 Vogue 3.5 EFI - Manual, gone.
2004 Volvo C70 2.0T convertible, had since new.
2007 Mazda MX-5 2.0 Sport Roadster/Coupé, had since new.
2024 Mini Cooper S cabrio, JCW kit, 2.0, DCT auto