This harkens back to the discouraged write() callable in WSGI PEP 3333 returned by the start_response() invocation. The PEP as well as Pyramid as a framework would encourage you to map the logic into an app_iter as Bert suggested.
I think you'll want to define a file-like object that you can write to and set as the app_iter. The question will be whether you try to do this by writing from a separate thread or in some other way because once you return control to the WSGI server to iterate on your app_iter then you are no longer in control - you'll need some buffer between where you're generating your parquet file and what you're returning from the app_iter. I don't think a simple tempfile is good enough because you want the app_iter to wait instead of stopping when it hits an EOF unless you know that you've reached the end of the buffer.