As I have found, the thermal switch, in my De Longhi Bambino heater can be re-set manually so that there is no need to buy a replacement. The button is in the back between the two electrical connectors.
To get at it on my Bambino, which may be similar on other De Longhi oil filled heaters, I had to unscrew the foot on the controls side, then two more screws in the metal bit behind and then unhitch the metal bit from a socket near the top.
Alan, February 2018