Land LHR 18:40 Tue 30 Jun → Prom 17:00 Wed 1 Jul. That's ~22 hours to recover, do laundry and glam up. Comfortable buffer — but don't book anything else for Wed daytime.
Late-June Osaka runs 27–31°C and sticky, with the rainy season just trailing off — much like Kyoto, but more concrete and less shade. Carry a fold-up umbrella and water; the aquarium and the metro are blissfully air-conditioned, and the food crawl is mostly after dark when it cools a touch.
Osaka bars, from a friend who knows