Bounties attract serious brainpower to the challenge.
Heater zones (circles) of ceramic cooktops that shine after the power is switched off for as long as the zone is hot and dangerous to touch or put things on. They could be illuminated in blue, white, or any other color other than red to differentiate that they're turned off but still hot rather than on.
Usually, electric cooktops have residual heat indicators, but they mostly look like this:
Tiny H letters or other symbols on the controlling panel in the corner of the cooktop. You can only notice it if you remember to check it the first place. Why not make it more obvious? I've never seen a cooktop with a very clear indication system as described in this idea, nor did I manage to find one online.
When the round zone is still on and heating, it shines red so you can't miss it, but once you turn the heat off, the color blends with the rest of the cooktop making it easy to forget. The circle could continue to shine (best in a different color) until it's totally safe to touch and put things on.
If not for adults, the obviousness makes it easier for kids.
Aesthetics - colorful, glowing circles on the cooktop would look nice and cozy, especially in the evening when kitchen lights are turned off.
How it works:
Implement heat-resistant lighting in the ceramic layer of the cooktop. Flexible led strips similar to these could be used:
Aerogels seem like perfect materials to embed such led strips in to achieve thermal protection while letting the light through at the same time, the fogginess of the gels would block some of the light and you'd get a nice glow rather than shining as a result. Twist the gel-embedded strips in a spiral shape so that enough heat would pass through the gaps for the heater to do its job.
Only the circumference of the heating circle could get illuminated to save energy, but it would be most effective safety-wise and, perhaps, in terms of aesthetics, to illuminate the whole circle. The brightness of the shining color could slowly wear off as the surface cools down. Another approach that would also be pleasant to watch is to make the color change as the surface cools down, for example - from red to orange, to yellow, to white.
A thermostat turns the leds on and off and makes the gradual intensity/color change.
In case the user thinks they don't need such a clear indication, they could turn it off with a press of a button (it could be named "extra safety indication" button or similarly).
An alternative approach I can think of would be to implement specific phosphorescent or another type of materials into the ceramic/glass surface of a cooktop that would convert the energy of IR radiation or/and heat into light and hence glow for some time after the heater is turned off. This would save energy, but it might be technically more complicated (if feasible) to achieve because it would require very specific materials that would have to also be heat resistant (or thermally insulated). Also, then there would be no way of turning the indication off.