Why do all medicines require storage temperatures below 25 °C?
People do not realize that the quality requirements for a medicine is rather high. We are talking about a complex mixture of more or less reactive organic compounds that are potentially sensitive to air, moister and light. Any reaction of the original ingredient is potentially biological active and harmful, and even simple things like recrystallization or coagulation can destroy the effect of the original mixture. 

The question "will they really spoil" makes no sense in the given context: if 99.999% of the cases not spoil, but there is a handful cases when things goes bad then the public goes banana. It took only one (purposefully false) paper to convince tens of thousands of people to go anti-vaccine, and decades till it dies out.  

If it happens with a medicine, it potentially kills the product, so easier to err (by huge margin) on the safe side.