What you don't eat cover with foil and transfer to fridge. If preferred, warm baklava up in microwave for 10-15 seconds before consumption.
Baklava can stay in the fridge for several days, although it rarely does. :)
For easier cutting, you can place baklava in the fridge for 30 minutes after you layer it (in this case you can butter that last layer right away).
A friend bakes hers at 400°F for a few minutes until it catches color, brings down the temperature to about 360°F and bakes it another 40 minutes. I haven't tried it this way, but if you report back.