The move by Cid Gomes, who briefly served as education minister in Rousseff's Cabinet, comes as it appears increasingly likely that Rousseff herself will be impeached on allegations she broke fiscal laws.
If she is impeached, Vice President Temer would be first in line to replace her, although his name has been cited by several operators in the snowballing probe into corruption at the state-run oil company Petrobras. In a sign of how much Brazil's political class has been tainted by scandal, the heads of the lower house and Senate, second and third in the line of succession, are also embroiled in the scandal. They all deny wrongdoing.
"My petition is Quixotic, but I am going to fight these terrible windmills for Brazil," Folha de S Paulo newspaper quoted Gomes as saying.
This is the fourth impeachment petition against Temer. Two have already been shelved and a third is "being processed" by the speaker of the lower house, Eduardo Cunha, a fellow member of the vice president's Brazilian Democratic Movement Party, or PMDB, according to the house's press office.
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Rousseff's chances of surviving the impeachment proceedings against her took a turn for the worse earlier this week when the PMDB pulled out of Rousseff's ruling coalition.
With a vote in the lower house expected as early as the middle of the month, Rousseff is scrambling to secure the 172 out of 513 votes she needs to halt the impeachment proceedings.
The latest filing against Temer comes a day after remarks by a Supreme Court justice disparaging the country's political class.