Hey!
For anyone seeing this thread asking the same question, here is the final schematic i've come up with.
It's essentially a schmitt trigger with a capacitor charging up to the target voltage creating the delay. I have tested it in reality and it works! Only replace the 100 ohm resistor in series to the capacitor to something like 1k ohm instead, this was only to make the simulation go faster.
//Benji
I'm glad the circuit does what you want it to, but it isn't a Schmitt trigger. There's no positive feedback and hysteresis: the on and off thresholds are the same. It's two NOT gates in series, which has a much higher gain than a single BJT, so the LED has a much sharper on/off characteristic, than you got with a single transistor. It can be made into a Schmitt trigger, by connecting a resistor from the collector for the right hand transistor, to the base of the transistor on the left. Please use designators Tr1, Tr2, C1, R1 next to symbols, it makes it easier to refer to components.
That circuit also has a few quirks which might be undesirable:
It uses more power when the LED is off, than when it's on, because the transistor short circuits it to turn it off.
The delay increases, with ingreasing supply voltage, because if the capacitor is charged up to a higher voltage, it will take longer to discharge to the 2.6V, required for it to turn off. Why 2.6V? It's because a transistor typically requires a base-emitter voltage of 0.6V to turn on and there's a potential divider consisting of 3k3 & 1k on the base, which divides the capacitor's voltage by 4.3, so the transistor won't turn off until the voltage on the capacitor falls below 4.3*0.6 = 2.58V, but there's no point in using more than one significant digit for the calculation, as the base-emitter voltage isn't that precise.
The delay is temperature dependant. The threshold is set by the the base-emitter voltage, which varies with the temperature. At room temperature it's around 0.6V, but it can vary significantly from hot to cold. The higher the temparature, the longer the delay, because it has a negative temperature co-efficient, which means the threashold voltage drops, with increasing temprature. The lower the threshold voltage, the longer it will take for the capacitor to discharge to that votlage.
The other circuits posted by Ian.M and me are somwhat sensitive to temperature and supply voltage fluctuations, but temperature is less of an issue.