Heat and humidity seperetely are two big killers of slides and negatives as are large fluctuations of the same; heat combined with high humidity is even worse.  Too low of a humidity is also bad for them.

Heat=accelerated deterioration, oxidation, and fading.

High relative humidity=softening of binders, fading, increased susceptibility to contamination from nearby stored chemicals etc.

Low relative humidity=shrinking and cracking of the binders as well as support material stress (curling)

Heat+humidity= the above + a risk for the growth of mold.

The ideal conditions for storage of mixed products (slides, negatives, and prints) is an RH between 30% and 50% without fluctuating more than 5% a day and a temperature of below 65F with fluctuations of no more than 5 degrees.

A good rule of thumb is that if most people aren't going to be comfortable in the environment then neither will your stored materials. i.e. the attic in August is very bad.