The funniest thng is I worl in a scientific polytchenic school but bringing a 15 kilos machineat work in the subway... Of course I could go to the lab and borrow some resistances.
I'm going to buy a PT100 and will tell you. If there's a problem with the PID that will be another story.

Thanks for your help

sensor ordered, fingers crossed

Those old boxes have their uses but I don't think that much functionality is needed in this case. Just a handful of resistors would be enough to settle the issue.

It occurred to me that one possibility is that while the display that resulted from the two resistances that were tried (48K and 3.3K) looked like a thermistor response it might actually be the controller totally confused with resistances far outside of the expected range. A couple of resistors, say 100 and 150 ohms, would quickly make it clear if a PT100 were the right choice -- assuming the controller is working.

The problem with cheap decade boxes is lousy switch contacts that can add significant errors at low resistances like one would need for a PT100.

If one exercises the switches and verifies the selected resistance they are tolerable.

A suitable range pot and a meter would also work, set the pot to a couple of temperatures and measure the resistances.

It depends on what you need. If precision is important I would imagine most of those boxes are lacking. Precision resistors are quite a bit more expensive than the usual 1% (or worse) variety. Then as mentioned you have contact issues as well. And if the lower value resistors aren't scaled up in wattage you can burn one up. But as I recall the boxes (they came in capacitance and inductance versions as well) could be quite handy at times. Pots are an alternative. They have their own issues.

But for verifying that it's a PT100 circuit you don't need high precision. In this case just one ±5% 100 ohm resistor would be pretty telling.

Well well well, I received the sensor today and the PT100 is a total failure. I just can't understand how a professional website sayd these are PT100 on these types of PID.
I can return the probe but that's not the point. I'm rather angry not to find an answer and to get some wrong answers (not from you guys).
I'm going to see my colleagues at the electrotechnic lab at work. Theay have tons of machines and components. I hope I will find my answer.
I just wonder if a 3,3k glassbead reacts differently comparing to the vishay thermistors.

I may have found the answer.

I founs this probe on a site :
https://products.italcoppie.it/products/p084001a-en/
First of all it looks very similar to the ECM ones. Second thing, the 3,3k value is given for 100°c and not 25.
And guess what, if I draw a approximative curve typical of a NTC probe (in red), at 25° we have circa 6000/6500 ohms so very similar to what the PID seller value found at 20°c. He measure 6300 ohms at 20°. The green point is what my pid shows at 25° ; 85° instead of 25
Don't pay attention to the blue curve that is for a 2,7K probe.
Does it sound logical?