To block the air from the radiator, you have to do it right, or the flow just bypasses your cardboard.....
Long-time north Canada resident and semiprofessional rad-blocker!
The best way is to cut a piece approx half the width of the rad and an inch taller, then move the rubber gasket aside, between the a/c condensor and the rad. Slide your blocker down between and leave the last inch protruding above (so you can pull it out next spring!)
Position it in the middle, so that some flow gets cooled on each side, but the area directly in front of the fan is shielded.
"They don't think it be like it is, but it do"