Looking at the original question, the requirement is to trigger the indicator light
after the dishwasher cycle has completed and it has cooled to a certain point.
That will need an "edge trigger" or two-stage sequence, so it's not falsely latched on when the device is initially set and the machine has not heated up.
It can be done with a 4093 using one part as a debounce and that capacitively coupled to two more sections configured as a bistable.
I'll try to draw up a legible version of the circuit to post soon.
Edit:
This is my concept circuit, using a CD4093 quad schmitt NAND gate and a few other components.
Ignore the extra bits on the gate symbols, that's just the way that program represents them..
V1 at the left is the power source, eg. a 9V battery.
V2 is the thermal switch.
The two gates at the right form a bistable or flip-flop circuit, which can be set to either state by taking one or the other input low.
(More info here:
https://en.wikipedia.org/wiki/Flip-flop_(electronics)#SR_NAND_latch )
When power is switched on, C3 holds the lower input low for a significant time (longer than the other capacitors take to charge and everything settle), which forces the bistable to the state where the lower output is high - so no voltage across the LED.
Initially the thermal switch is off, so R1 charges C1 and the output of the A1 gate switches low after a short time.
(C3 should hold the other input of the bistable low for longer than that, so nothing happens).
When the thermal switch closes, C1 discharges, A1 output goes high.
Nothing else happens.
When the switch opens as the machine cools, C1 charges again, A1 output switches low and a pulse passes through C2, triggering the bistable to change state so the upper output is now high and the lower one, connected to the resistor and LED, is now low - the light comes on.
It will stay in that state until power is removed.
It needs an on-off switch in the battery connection & it should have a capacitor between power and ground.
R3 and R4 should also be a rather higher value in retrospect, 47K or 100K would be reasonable.
The only steady-state current draw apart from the 4093 (which takes miniscule power) is R1 while the thermal switch is closed, and the LED circuit once the device is triggered.
An ultra-bright LED could run from a higher value resistor to reduce current consumption further; I have some white ones that are painful to look at with less than 1mA current..
If anyone sees any daft mistrakes or has any improvements, please comment!
Edit 2 - I just realised the spare section of 4093 could be used to make the LED flash on completion, rather than just light continuously.
Use this circuit:
https://lh5.ggpht.com/_ghw-EsIYo58/TTtzsVVgCnI/AAAAAAAAAFQ/u9XaBTjbBOs/s640/AboutSchmitt02.gif
And connect the "control" input to the upper gate output on the latch.
The LED & resistor again between the [added] gate output and positive power.
Something like 1M and 1uF should give a moderately fast flash.