I can't answer the legs question, because I always wear long trousers, all weathers, but as someone who spends half his life (gladly) on a bike, I tell you a few things I find important.
Wear a hat in strong sunshine. Carry wrap-around glasses for when you are cycling near trees etc, or where there are many insects. A fly smacking into your eyeball is very painful. Breathe through your nose, not open mouth (or cover it with a hanky) - again a fly, or worse a wasp, disappearing down your throat is very very unpleasant.
Carry a spare inner tube, tyre levers, and mini-pump when venturing far from home. Walking a bike with a flat tyre 4 miles home is a drag. Better, fit 'puncture-proof' tyres, such as Specialized Armadillo. I've had these on one of my bikes for 3 years now, never yet had a puncture. Pump your tyres up HARD especially for road use. I run at about 50psi. The ride is smoother and a hard-inflated tyre is less prone to puncture. Cycle with the ball of the foot, not the instep or heel.
Never be ashamed to get off and push when the going is tough ! I took my bike to Box Hill last week, I challenge anyone to cycle all the way up from the station to Polesden Lacy, especially in this heat.
Great fun cycling, liberating and predictable, no traffic jams......