Of course temperature can't jump like this. And it seems like EM interference, though also you can get similar effect if one of wires in 3 wire scheme has unstable electrical connection and due to vibration it breaks.

The thing you should do is to check grounding first of all.

Generally i agree with weddra. He writes about an assumption that 2 wires, which are laying close to each other, have same reaction on EMI. Not relating to 4 wire RTD scheme we can tell, that if EMI causes potential growth at wire A of 1 volt and on wire B also 1V we can treat this as no EMI took place as we measure voltage = difference between wire A and wire B potential.

Twisting wires in pairs just allows 2 wires to be even closer.

Also i would ask thread starter to identify sensors used, because some PT100 sensors are isolated, others not.