I've put amplifiers on their sides before and had no issues. In theory the heat syncs would likely be laid out in such a way that the heat will rise up away from the components. So perhaps putting it on its side would cause the heat to rise through them instead of up and away, causing it to stay hotter longer? . Have a look inside to see where the heat syncs are and if possible put it on the side that best locates them as high as possible. Maybe put a USB powered cooling fan on it to get some air moving inside.

Craig.