I'm lucky, I've never had flu. I've had some very heavy colds, but never flu. Until recently I have never taken anything for a cold other than paracetamol to alleviate the headache symptoms. I have resorted to cold remedies in recent times, but that is mainly because they contain decongestants.
I tend to go to bed early when I have a cold, but that is simply because I am run down and tired. I drink lots of sweet tea, but again that is because I feel run down and the glucose gives me a lift; but this feeling is very much a personal perception. I don't think taking glucose speeds up the recovery process as I find sweet tea only really makes a difference to how I feel towards the end of the cold when I probably feel quite low and am in need of energy.
As for sweating out the cold/flu, I think the process of getting warm just makes people feel better when they are run down and actually does not help to speed up the process of getting well.
My own experience of having a cold is about making myself feel comfortable rather than speeding up the body's immune response. The latter, my body does in its own time, and all the sweating, sweet tea and keeping warm make no difference to how quickly I can fend off the virus.