My personal trainer said it this way; (not a quote) Muscles are like rubber bands so ... so imagine what would happen if we tried to stretch a rubber band that has been in a ice water vs. a rubber hand that has been in simmering water. The band in simmering water will stretch longer and retain it's shape, elasticity, and strength while the rubber band in ice water will likely break, become weaker, lose it's shape, or it's strength.
Now, imagine your quads being that rubber band and you pulling on them while stretching one early morning fresh out of bed, preparing for your run; the stretch will hurt more and we've been taught to think ... "mmm good it's stretching a lot" when in actuality the muscle is saying Hey dummy! I am too cold for this and most likely exhibiting some micro tearing or injury vs. muscles that are warmed up not tearing. Yes tearing is good when trying to build muscle, but it should be occurring during exertion to muscles that are warmed up.
Also, Please drink plenty of water as it will help to relieve the soreness in your muscles by carrying away the lactic acids in the system. Breath while you are stretching at all times so that your blood continues to feed those muscles plenty of oxygen. Remember to cool down after you exercise instead of just heading in to the shower. Food we eat directly after hard work out is digested 30-40% more efficiently and fed to the muscles if high in protein so eat a small meal after your workout.