What could cause a random redness and warmth in knees, without any pain or swelling that comes with it?

Knee redness: Knee redness and warmth without pain, tenderness or swelling suggests skin reactivity ? To friction or irritation from clothing. Cellulitis doesn't appear likely to be present due to transient nature of your symptoms and absence of spreading redness and simultaneous involvement of both knees. An allergic reaction also is unlikely due to lack of itching and ongoing eruption.