Then you need to break up your problem into processes. Python doesn't really do multi-threading (hopefully that changes with the GIL going away), but most things can scale reasonably well in a process pool if you manage the worker queue properly (e.g. RabbitMQ works well).

It's not as good as proper threadimg, but it's a lot simpler and easier to scale horizontally. You can later rewrite certain parts if hosting costs become a larger issue than dev costs.