Unicorn + Rails + Large Uploads

I'm trying to allow for large uploads when running Unicorn on Heroku with Rails but I've realised that any large uploads might take longer than the timeout period for a Unicorn worker. This will mean (I've seen this happen) that the Unicorn master process will kill the worker uploading the large file and the request will timeout (with a 503 error). Without removing or massively increasing the time