Induction cooker on a wooden table

I use a Sunartis E514 digital household thermometer on an induction stove, and I get normal readings.

I can't say it is the best thermometer out there, as it is a bit slow. The specification is 4 to 10 seconds measuring time. From experience, it doesn't need 4 seconds to change the display when immersed in hot liquid, but while it gives you the temperature with 0.1°C precision, I guess this temp is slightly lagging. That can ruin a batch of candy or dark chocolate, but these are still doable if you are mentally accounting for the lag. It is great for everything else. The low price is another advantage.

I can't promise 100% that it will work with any induction stove. Mine is a small portable one, and maybe its magnetic field is weaker than that of a full-sized stove. For temperature-sensitive applications, I usually cook on 500 Watt, but I've had the thermometer inside (also very close to the bottom of the pot) at higher settings, so I hope it will work. Nevertheless, it is probably a good idea to get it from a place with good return policy.

The upper surface is glass, so I clean it like a normal Ceran stove: A special ceran cleaner when a cloth isn't enough, a sharp blade for specks, a gentle abrasive (like Cif) for stubborn spots which won't get away. The sides of mine are alu, but I don't bother getting out a different cleaning agent for that, just continue wiping with whatever I used on the glass.

I have never opened mine to clean the fan, and suspect that it will void the warranty. But if needed, I would handle it like a PC fan: open the case, use compressed air to blow it clean. Trying to wipe the fan could decenter it. It won't make the blades perfectly smooth, as the humid kitchen air tends to turn dust to clingy grime, but it should remove the bulk if the fan is too full to work efficiently.