Case covers give extra protection against the weather and add some extra storage room to the case. Some are available with special insulation material to keep the temperature consistent for a longer period of time. Don't overestimate how long the temperature can be held.
Some also include integrated backpack straps, making attaché cases look less like computer or business carriers, which may reduce the risk of theft. An additional strap can often be attached, so it can also be carried as a shoulder bag.
Attention: As black covers are the most popular ones consider some bright colors. Dark covers are hard to see in the dark. As a pedestrian or cyclist, you can easily be overlooked in traffic. A bright color or additional bright reflector will be very helpful.