Seems a strange request, can anyone let me know what the procedure is to temporarily import a rifle into the US?

Will you be importing the rifle for a hunt, repair, sale ?

Repair. I travel to the US to do marketing and can carry it in.

I remember hearing that one can no longer import Mausers with thumb cuts in the receiver. Is this true? How about if it's only for repair?

Wink, there was a court case about that .The Gov't assumes all thumb cut rifles are military.The was a shooter who had a civilian Mauser with original thumb cut and documents to prove it. He won his case .
It's all sillines of course but check carefully to save yourself trouble.