Question

Why at high temperature electron of pi bond moves to C=C part of ether in claisen rearrangement.

Answer 1

It's similar to the whole keto-enol tautamerization and hydrogen stability (think back to hoffmann rule). Similarly, this also adds stability to the molecule itself with an extension of the carbon molecule itself. The reaction(s) proceed differently depending on the molecule itself. I think I only remember doing claisen rearrangement with ethers and carboxilic acids and a few aromatics. I'm not sure about any other type of molecules such as amines and poly-substituted aromatics.

Answer 2

How can an extension of carbon molecule bring stability

Answer 3

resonance stability. Think of benzene.