The appeal, filed by Rousseff's lawyer Jose Eduardo Cardozo and seen by AFP, demands "the immediate suspension of the effects of the Senate decision."
The Senate voted yesterday to convict Rousseff on charges of having illegally manipulated government accounts, stripping her of her office and replacing her with Temer, her bitter enemy and former vice president.
Cardozo's appeal asks for "a new trial" during which Temer - who was sworn in as president up until the end of 2018 - would be downgraded to interim president.
Rousseff was convicted by a two-thirds Senate majority of taking illegal state loans to patch budget holes in 2014, masking the country's problems as it slid into economic disarray.
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Senators voting for her removal said she had contributed to Brazil's economic crisis and acted with criminal irresponsibility.
Rousseff, from the leftist Workers' Party, denied doing anything illegal and claimed to be the victim of a right-wing coup d'etat.
Rousseff left office with rock bottom ratings after being blamed by most Brazilians for the country's slide into double digit inflation and unemployment. She has also been tainted by the revelation of a colossal embezzlement and kickbacks scheme at state oil giant Petrobras, although she has not been accused of participating herself.
Temer, from the center-right PMDB party, rode that dissatisfaction all the way to the presidency in an impeachment process he describes as giving Brazil a chance to put its house back in order.