Warming up is necessary. I know someone who played Prokofiev's seventh sonata without warming up, and after that he couldn't play for 6 months. Warming up with trills, scales, arpeggios, some bach inventions will do the trick. Contrapunctus is absolutely wrong on this one.
it's possible that it was a build up of tension from years of a habit playing heavy pieces like the prokofiev sonata without proper warm up.
yes it's physical... only if you integrate it with the mental. otherwise, it's not warming up for the sake of "heating up" the fingers only. it's actually also for the brain. u know, this is how a five note scale feels like, a c minor scale, arpeggio... etc. once you get your brain into "piano/practice mode" then everything else will follow smoothly without tension. then you can now start with solving technical and musical problems.
so i guess, warming up with scales, arpeggios, trills will do the trick just as a lot of us here would say. only that IMO, we shouldn't take the phrase "warm up" literally as warming/heating up the muscles. it's like we would like to familiarize ourselves with some musical stuff (theory, sounds, etc.) before we play/work on some music to avoid building up physical tension (we build up physical tension when we are not familiar with something mentally, wc could lead to injury if done in years, like the example of prokofiev sonata above... don't we get physically tensed performing on a bad piano that we have not rehearsed with?).
so/but, i'd like to say that warming up is 40% physical and 60% mental.
in cold places however, you mght want to do what Glenn Gould did, soak in lukewarm water... or hair dryer for Stanislav Ioudanitch (spelling?) now this is purely a physical situation and holding a hot cup of tea will help... but you don't need to tire yourself too much of scales and trills before a performance just to heat up in a cold place.