Any closed simply-connected 4-manifold $M$ and its exotic copy $M'$ are h-cobordant by a theorem of Wall. Thus $M\times S^1$ is h-cobordant to $M'\times S^1$ which is in fact trivial by high dimensional s-cobordism theorem. So they are in fact diffeomorphic. And similarly one can generate more examples I guess in other dimensions.
Anubhav Mukherjee
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