"When the show first came out, there were white people and black people talking about [how] the Huxtables don't really exist, black people don't really live like that," Warner said in a 2013 interview.
"Meanwhile, we were getting tens of thousands of fan letters from people saying, 'Thank you so much for this show.'"
After The Cosby Show, Warner appeared in several other television programmes including Malcom & Eddie, alongside comedian Eddie Griffin.
Griffin paid respects to him on social media after his death, writing "R.I.P. King" and "My big little brother".
Warner had guest appearances on The Fresh Prince of Bel-Air and Sesame Street. More recently, he played AJ Austin, a cardio-thoracic surgeon on the medical drama series The Resident.
Warner also won a Grammy for Best Traditional R&B Performance in 2015, alongside Robert Glasper and Lalah Hathaway for their cover of Stevie Wonder's song Jesus Children of America.
His spoken word album "Hiding In Plain View" garnered him another Grammy nomination in 2023.
Last year, he started a podcast - "Not All Hood" - which discussed mental health in the black community.
Former co-stars and fans has been posting their tributes to him online.
Basketball star Magic Johnson, who appeared in an AIDS awareness video directed by Warner, wrote that he and his wife were "both super fans of the hit Cosby Show and continued to follow his career" over the years.
"Every time I ran into Malcolm, we would have deep and fun conversations about basketball, life, and business. He will truly be missed," Johnson wrote.
Actress Jennifer Love Hewitt called him "a gentleman" and "an incredible talent".
Actress Vivica A Fox posted that she was stunned and saddened by his sudden death, writing: "Thanks for ya gifts, king."
Tracee Ellis Ross, who starred with Warner on Reed Between the Lines, also mourned him, writing: "My heart is so so sad.
"What an actor and friend you were: warm, gentle, present, kind, thoughtful, deep, funny, elegant. You made the world a brighter place.
"Sending so much love to your family. I'm so sorry for this unimaginable loss."
Actress Taraji P Henson posted: "Malcolm, we grew up with you. Thank you for the art, the wisdom, the grace you gave us!!!!!
"You left the world better than you found it. Rest easy, king!!!! Your legacy lives far beyond the screen."
Actress Niecy Nash posted that she had recently spoken to Warner.
"We talked about how happy we both were in our marriages. Damn friend. You were cornerstone of The Cosby Show.
"We all loved Theo! Never to be forgotten. You will be missed. Rest Easy."
Georgia Senator Raphael Warnock also praised Warner, writing in a post: "For me and so many in my generation, Malcolm-Jamal Warner was a part of our childhood, a brother whose character 'Theo' felt like one of my own.
"May God grant peace to his soul, strength and grace to his grieving family."