As brought out in the court scene with fellow NBC alum Ana Gasteyer, Thompson was essentially playing himself in the episode. He was on television (NBC's Law & Order) and he is a lawyer (Vanderbilt Law, 1967). In the episode, he was (fictionally) representing Hugo Chavez, who (fictionally) appeared via videolink in some rather humorous vignettes, including a reference to Lindsay Lohan. In real life, Thompson has lobbied for the Tennessee Savings and Loan League and the Teamsters Union's Central States Pension Fund.
In an odd way, CBS captured some of NBC's investment in the character "Arthur Branch." Thompson wasn't playing Branch on "The Good Wife" but he was playing the actor who portrayed a character like "Arthur Branch" of NBC's "Law & Order."
Fred Thompson in “The Good Wife” tonight