from datetime import datetime
import requests
now = datetime.now().strftime('%Y-%m-%d_%H-%M')
string_that_you_need = now + '.mp4' # Сейчас это выглядит, как "2015-04-29_10-59.mp4"
request = requests.get('http://site.that/you/need/%s' % string_that_you_need)
f = open('file.mp4', 'wb')
f.write(request.content)
f.close()