Did marlo thomas wear wigs on that girl?

There was a book about That Girl that came out a long time ago, that stated, after the first season, she was letter he bangs grow out, but, Clairol still wanted her to have bangs, so, they made her wear a 'bangs wig!' Several seasons later she just let her hair remain parted down the middle and the bangs wig was done away with! She is Lebanese and Italian so she does have amazing, thick, natural hair of her own!