In order to accomplish this, you would need a logic circuit. A little big for a small device, but it would be doable with a larger case.
I think the easiest way to do this would be to incorporate an and gate in the circuit. A constant signal voltage (1) would be applied to one of the inputs, the other would be the signal from the detector, which in this case, I would think some kind of NTC (negative temperature coefficient thermistor might work. When the thermistor heats up to a certain point, it allows enough voltage through to the logic input of the and gate to turn the 0 into a 1 (so there would be 2 1's on the inputs) which would allow a 1 output. An LED would then be wired in series with the output.
It would take a lot of experimenting with thermistor placement, but doable.
Another option would be to incorporate a current detection circuit, as current falls as temperature increases.
Either way, it would be next to impossible to situate such a circuit within the atomizer body