First thing's first:
Do you have other people that use your internet? If so, make sure they're not downloading a bunch of stuff!
Secondly - Powercycle your modem! Go to the modem itself (lil box with blinking lights that has one of those coaxial cables (the one thats normally used for cable tv) and UNPLUG the power, leave it for 30 seconds, plug it back in - give it a minute and try again...(Reboot your computer)
Optional - even though it's only specific to the time of day - this might help you overall, but not remedy your 6am issue (thought you might want this as every KB/sec counts hehe!)
If your internet is still slow - clear your temporary internet files! Every website you visit - every little picture and word is SAVED to your computer, so that if you go back to that website - it loads a bit faster... WELL there is such a thing as too much of a good thing - eventually if you have tooo many internet files (and I mean it takes a lot) it takes time for a computer to go through all those files and everything feels slooower.... If you're running Internet Explroer - go to 'Tools' at the top, Internet Options, and click on Delete Files. It may take a few moments but it's worth it.
If it's still absuredly slow - call your Internet Service Providor - as it will likely be something to do with the lines that run your service... It happens where your signal strength may be TOO high or TOO low (this happens gradually over time, and weather/temperature can effect the lines) and they may need to send someone out there to put a filter on your line if it's too high, or a booster if it's too low :) So don't hesitate to ask them how your signal strength is looking!
There are a few factors that will still affect speed but those are the culprits.
Hope this helps! *thumbs up*