Everything in color (excluding some steps of the Kodachrome K14) is done at 100 degrees Fahrenheit with the exception of push/pull processing in film chains which cannot change the time. Cross processing means you run the film through a different process at specification. For example, if you want to run E6 film in C41 process you simply act like it's regular C41 film. This process gives you weird images, depending largely on the type of slide film used. I have never tried it. The times/temperatures don't change. Bleach bypass means you don't bleach, it will give you higher contrast and lower saturation. For push processing you extend the C41 time by 30 seconds for each stop you wish to gain. This is all very standardized between films.
Temperature is most critical in the color development stage because it changes how the CD interacts with the dyes. The temperature is less critical with the B+W developer (in E6 processing) and not critical with bleach and fix. I'm not entirely sure about washing at different temperatures but I assume that the wash is less efficient at lower temperatures. You have to be careful not to cause reticulation by changing temperatures too rapidly. Kodak does state that the Bleach and Fix steps can be carried out down to 70 degrees F, however you might consider extending the time of the bleach to ensure bleach to completion.