I would suspect that a starter not working in these conditions is a bad starter, no matter the country of origin.
You may also wish to check your battery cables and terminals for corrosion, and check the charging system to make sure it is putting out properly too.
If I truly believed heat was the issue, and the starter was to blame, I would stick the starter in the oven to heat for a while before bench testing. The lowest typical oven setting is 150-175, which I think would be perfect. That should tell you everything.