I put my fermentor in a large bin filled part way with water. The water helps to stabilize the temperature, since it takes time for a swing in air temperature to warm or cool that large a volume of liquid. With that range, you should be fine.
The only problem with a cooler, without anything to cool down the fermenting beer, is that heat produced by the yeast will be trapped, leading to greater temperature increases during the most active phase of fermentation than if the fermentor were simply sitting in the open room.