How do temperature and pH affect enzymes?

#"pH"#: The amino acids in biological systems have substituents known as carboxyl functional groups and amine functional groups. These functional groups are capable of interacting with the surrounding environment, and, as such, are impacted by the charges added to the solution by the ionic compounds contributing to the #"pH"# of the solution.

Enzymes have a three-dimensional conformation that they fold into post-translation, meaning that any form of interference with this conformation may alter the function of the enzyme, whether changing its function entirely, or simply inactivating it. These interactions usually involve what are called organic mechanisms (which are way to long to explain here). Enzymes all have their own optimal #"pH"# range, wherein they function most efficiently. Outside of these values the enzymes tend to become less functional.

As for the temperature of the enzyme:
Enzymes, as noted above, have a three-dimensional conformation. This is partly due to hydrogen bonds between nearby amino acid side-chains. When energy is added to the system, however, these hydrogen bonds become less attracted to each other and less capable of holding the 3D structure of the enzyme (due, as you correctly noted, to the increasing kinetic energy within the molecule). This results in an event known as denaturing. This event describes the unfolding of the protein.

Note: Some proteins (normally very simple ones) may resume their normal function post-denaturing (after the energy in the system has returned to the optimal functioning level). However, some of the more complex enzymes in our body require the assistance of other proteins known as chaperonins to fold properly following translation. These proteins tend to lose their functionality entirely following extreme temperature spikes, as they will no longer be able to reform.