Well, "conditions in the park" is really a broad topic, because elevations vary.
Kalispell is at 3000 feet. Apgar is about 3200 feet, so weather is much the same. Avalanche CG is 3500 ft, and the hike to Avalanche Lake (4000 ft) is beautiful.
St Mary is higher at 4550 feet, and Many Glacier is at 4950, so the east side will be colder. And if you want to hike trails at even higher elevations, you'd likely run into snow. So it all depends on where you want to go in Glacier. I'd say if you find it too cold or snowy on the east side, loop around the south end of the park and stay on the west side where it should be fine.
I was there the year they set a new record for lateness of opening the Sun Road (July 13), and traveled to Logan Pass on that day. Short sleeve weather at Many Glacier, but at the pass it was pretty chilly with huge snowbanks. Still I got some great pictures of a bighorn up there.
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