BGR reports that Apple will be seeding the third beta version of iOS 7 on July 8th.
Apple had seeded the first beta version of iOS 7 to developers immediately after the WWDC Keynote on June 10. Apple released the second beta version earlier in the week, on Monday, June 24 just as BGR had reported.
Based on historical data, July 8th for the third beta version seems a little early as Apple released the second beta version of iOS 6 in 20 days and the third beta version of iOS 5 in 17 days.
But it seems quite likely that it will be release in the week starting July 8.