issues of a bad radiator please-

Hi folks can anyone advise issues with having a radiator that's kaput. My car sometimes gets warm when idleing. Can a bad radiator cause this? I drove to nottingham on sunday and car was fine on motorway until I hit traffic when almost home. My radiator does look knackered tbh and has a few stains on it. Fan does kick in when it does get warm and then I park up and allow it too cool. Heater is hot and no other issues. Can anyone advise?

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