With the following command, I can retrieve the output in the temp file :
Start-Process powershell -Verb runAs -ArgumentList "C:\Users\Florian\Documents\Test\script.ps1 -Install *> $Env:TEMP\temp_python_output.txt"
But not with this one :
Start-Process powershell -Verb runAs -ArgumentList "C:\Users\Florian\Documents\Test\script.ps1 -Install | Out-File -FilePath $Env:TEMP\temp_python_output.txt"