I've taken the classic Fuzz Face circuit and added optical temperature compensation. This ensures that the output stage is biased at half the supply voltage regardless of variations in the transistors, particularly those caused by temperature. Tweaks: Obviously, one could make the bias point adjustable, but it sounds fine set to halfway.
One could add a resistor across the LDR to set the maximum value which would also cut current consumption slightly as the LED would go darker in response. This achieves lower minimum values too. Try 47K.