Ideally, your art auction will be held at a time of year when the most people possible will be able to attend. This typically means scheduling it either in the summer or during the holidays. Ideal months, then, to start your art auction: December, May, June, July and August.
Again, the priority here is people. The more people who attend your auction, the better your chances of seeing high bids on more items. This means that scheduling your auction for a Wednesday or a Monday or any other day during the normal workweek probably isn't the best idea. Try starting your auction on a Saturday and continuing through Sunday. The weekend, without a doubt, is best. The only exception would be if your auction is going to be at a school or in an office building or convention center that tends to be packed during the week but empty on weekends. In those exceptional cases, you'd want to schedule the auction to start during the week, when more people will be filtering through and walking by.
Again, the time of day depends on the number of people who will be able to attend. On weekends, it doesn't particularly matter; start sometime in the morning and end in the evening. If you're going to hold it during the week, though, there are other questions to consider. Will scheduling the start of the art auction during normal work hours interfere with most people's ability to be there? Generally, it's best to start the auction just after work hours are ended--perhaps around 7 p.m. There are exceptions, though. If you are holding the auction somewhere that is buzzing during work hours, it may be best to begin the auction at lunchtime.
According to one study, the most popular day to end an Ebay auction is Sunday. This suggest that an art auction online is best timed so that it ends on Sunday, thereby increasing your chances of walking away with large bids.