I think the cold hand is much more plausible than the hot hand. You can't make your eye sight better, brain faster, muscles stronger for some arbitrary period of time like you drank a potion in a video game.
I do believe in the cold hand. I believe the randomness can get to you, and get in your head and cause you to press the issue. I also believe good athletes in the right state of mind can prevent and shorten these down turns. Baseball is mental, and sometimes winning that battle is just mainting focus while you let the other guy fall apart. But I also believe in the stats as well, but I also believe that the smaller a sample size the more deceiving the stat line. That 0-20 could entail 4-6 hard hit line drives right at someone and 1-3 amazing plays made against you. That 10-20 could entail 1-2 HR's against a guy was losing his stuff, an infield hit, a misplayed flyball, a weakly hit blooper turned double, and a soft liner that found a hole.
In our innate thirst for pattern recognition I think we look at the small sample size and read into it too much. Again, I acknowledge the mental side of the game, but the long term statistics prove at the very least we often over estimate the hot/cool hand.
While a stat guy at heart, I also believe incorporating the good old eye test at times too. If a guy is 0-20 with 10 k's and 10 weakly hit balls. I'd consider giving him a day off or dropping him in the order. But if 10 of those outs were scortching hot liners, and a a robbed home run ill bat that guy 3rd if it's Mookie, even if it's the bottom of the 9th and we're down 3-2 with two outs.