Supernaut's Cars - E36 323i / mk3 Megane / S1 Land Rover

[Tayne]

Does your one have a hedgehog?

[Supernaut]

Not that I'm aware.

It has this style of climate control:

It seems that the fan (I've tested it and it works) blows into an air temperature sensor built into the unit. Hmmmm.

[SiBriers]

Not sure the hedgehog would explain that behaviour (that's usually certain fan speeds not working or the speed wandering).
On E46s, the top centre fan outlet has a heat control - without air con this could be as you describe - ambient air until the thermostat opens and hot coolant reaches the heater matrix.
Also possible that the heater control valve (on the passenger front inside shock tower on E46) has locked up or is getting stuck - supposed to blend the amount of engine coolant the heater matrix sees.