Chemical reactions are based on collisions, but only those with the right amount of energy and the proper orientation give rise to them. If just one of these parameters deviates enough, the reactants will just bounce off. Within a cell, collisions between reactants are likely to happen, as one molecule is likely to collide with its enzyme within a second,[1, p. 6] but not in the right orientations. Enzymes through a moderate affinity to the reactants, place them in the right orientations.
Now, where does the energy come from? The molecular "storm" of water molecules around does have quite a bit of kinetic energy, but as collisions with them come from all directions, they usually cancel each other. When ATP hydrolyzes, about 0.36 eV of energy are released (5.8·10^-20 J), and the molecules around it vibrate. I suppose that this is because once the chemical bond is broken, the repulsive force between ADP and phosphate is very strong at such a close distance, violently pushing whatever molecule they find on their way. The amount of energy released has 14 times the average kinetic energy of the molecules around it, so it is the equivalent of locally heating a molecule to 3,900 ºC. Naturally, if the hydrolysis happens within an enzyme, it vibrates like crazy and induces a conformational change. If the enzyme has reactants bound to it, they are likely to collide with the right amount of energy.
Interestingly, the molecular storm is powerful enough at 150 ºC to break down ATP. This is why scientists do not expect to find any hyperthermophile living at such warm temperatures. Currently, the archeon Pyrolobus fumarii holds the record, being able to survive up to 122 ºC, but its optimal temperature is 113 ºC and "freezes to death" at temperatures lower than 90 ºC [Wikipedia].
 Goodsell, D. "The Machinery of Life". 2nd edition. Springer. 2009.
 Hoffmann, P. "Life's Ratchet: How molecular machines extract order from chaos" Basic Books. 2012.