The material is described as a urethane methacrylate. This is probably also moisture sensitive (depends on how/if the molecule is "capped". In any case it described as "anaerobic", so putting it a bag in a fridge might restrict the amount of air it comes into contact with, i.e. it will start to cure. On the other hand it might attract moisture, also not good. As to the difference between 5 and 8°C, go out on a cold morning and see when you can see your breath condense in the air when you exhale. All of these data sheets from manufactures tend to the cautious.
What you say about "chemical reaction rate doubles for every 10 °C rise in temperature" (Arrenhius) is a rule of thumb, it depends on the activation energy of the reaction and whether it is endothermic or exothermic.
This stuff comes in a bottle designed to allow air in to stop it curing prematurely but perhaps keep moisture out. I´m not sure whether throwing the bottle in the drawer is better than sticking it in the fridge.
The viscosity in use shouldn´t be a problem, its just the shelf life and storage.
In any case most methacrylates depolymerise if heated to ~150°C, so the polymethacrylate bit can be softened and will decompose with gentle heating (work in an open, well ventilated area ).