He cannot claim commuting or parking expenses unless his temporary assignment is outside your metropolitan area,
That is, the fact that it is a temporary job is irrelevant if he comes home every night.
https://ttlc.intuit.com/questions/1899669-can-i-deduct-commuting-expenses-like-gas-mileage-or-toll-f...
As an example, this case from several years ago is still valid:
https://www.claconnect.com/resources/articles/tax-court-nixes-deduction-for-travel-to-temporary-work...
