Do those who are lenient have something to rely on? Yes, I’m talking about a case where the thermostat apparently works after opening the door in order to bring it back to the required temperature.

Yes, but only with difficulty. It is an inevitable result that is beneficial to him, involving a prohibition that in my opinion is Torah-level, but in the opinion of the majority is rabbinic. Beyond that, I think there is room to view this as unintentional involvement rather than merely an unintended act. You are engaged in opening the door, and at the same time something else happens. As several halakhic decisors wrote about someone who walks near a lighting sensor and activates it—that this is not merely an unintended act or an inevitable result, but rather unintentional involvement. He is not engaged in activating the sensor, but in walking. Of course, distinctions can be made.

What about the fact that an oven looks like cooking?

Has a Sanhedrin been established and I somehow didn’t hear about it?!

Rabbi, why would a Sanhedrin need to be established for this? If indeed using an oven is considered a normal way of cooking, why wouldn’t that fall under the definition of “looks like cooking”?

Because that would be a new decree. It is forced to squeeze a new situation into an existing decree. Like the claim that riding a bicycle is forbidden lest one come to repair it.

But the decree is general, covering all forms of cooking, isn’t it? Why should a new situation that fits the criteria of the prohibition not be considered part of it? After all, if ovens had existed in their time, it seems quite obvious they would have explicitly included them too. Most, if not all, rulings made when there is no Sanhedrin are based on comparing one matter to another, aren’t they?
It’s like if a new animal were to come into existence—one that didn’t exist in their time—but it met the criteria for a pure animal, it would be considered pure, wouldn’t it?

Thank you very much, Rabbi, for the answers.

There is a difference between Torah-level laws and rabbinic laws. In Torah-level matters we compare one matter to another more than we do in rabbinic matters. Therefore, if the reason for a decree no longer applies, the decree is still not nullified—both for stringency and for leniency. For example, nobody would think to forbid soy foods, like Tivall schnitzel, with milk.

As for the signs of purity, that is not relevant to our issue at all. There, the signs themselves were given, and the entire application was left to us. This is not a matter of comparing one case to another.

Regarding soy foods, in my opinion that is not comparable, since the appearance of the raw material is not similar to meat at all. Besides, there the definition itself is specific to poultry, not to something that merely looks like meat—fish, for example, is not included. If a new type of bird were to come into existence now, one that didn’t exist in their time, then indeed one would have to forbid cooking/eating it with milk, no?

As for the signs of purity, I gave that as an example of a situation where once the conditions of the commandment / prohibition / decree were established, they do not remain fixed only to what existed in their time; rather, “new” things too, so long as they meet the criteria, would have the prohibition apply to them.