It indeed does get pretty cool the further up you hike.  The hiking that I did, wasn’t bad (and i’m Canadian — however I had just come from the extreme heat of Venice), but I still had pants and a coat.  If you plan on going up Jungfrau (on the train, not hiking), there will be snow up there all year round.

I think you’ll be fine.  I was in Interlaken in Mid-June of 2005 and we didn’t need any heavy clothing.  It was actually pretty hot in the city and around the valley as we visited the lakes.  We swam in the lakes, along with plenty of the locals, but we thought the water was pretty cold.  We also went up into the mountains and stayed in Gimmelwald.  While up there it felt cooler, but still not cold.  At around 5,000 feet up the weather was still comfortable to walk around in shorts.  We went hiking above that and got upto around 8,000 feet.  Up here it was much cooler.  I was in Shorts and a Tee Shirt and for much of the hike up I even had my shirt off because it was so hot, but near the top, and espcially when the clouds moved in, it began to feel pretty cool.  But it was nothing unbearable.  You’ll be fine.  Don’t bother lugging around all the heavy clothing.    

Just came back from Interlaken two weeks ago, and hiked through the alps. We only had jeans and full sleeve t-shirts on, and it was fine. It did get a bit breezy for a bit, but if you have an upper or a fleece to throw over your shirt, you’ll be fine. Travel light and don’t worry about thermals, unless you plan to travel in September or later.

One thing you may want if you’ll be out hiking for several hours is a waterproof jacket. 
Or at least something other than a cotton shirt to keep the moisture away.  I was hiking
near Grindelwald a few years ago about 4 hours from town and got caught in a fast moving
thunderstorm wearing only a cotton t-shirt.  It was a numbingly cold hike back down the
mountain.  In my experience this happens quite often at altitude so be prepared.

Arise…arise!!  I resurrect you, old topic.
 
I won’t be making my way through Interlaken and the like until July-ish so I’m sure I’ll be fine temp-wise (and enough summers in Colorado have taught me about fickle alpine weather!), but I do have a question about actually camping in the alps/Europe in general.
 
I’ve perused the other topics but they seemed a little lacking in specific details, as were the supplement websites.  They were helpful, but firsthand advice is the best.
 
I want to do this trip on the cheap.  When I’m not in major cities, I’m A-OK with pitching a tent in a field, and on nice nights sleeping under the stars.  Locals would know the best places for this (if it’s different than the campsites).
 
My questions are about tents and bags.  My tent is a 5 lb Apex 2XT…which seems like a pretty good option.  They don’t come a whole lot lighter really.  What about bags?  You always pack for the worst, so what kind of weather will I be getting in the alps?  Let’s say I wanted to camp at 8000 ft or so, just to factor in all the extremes.  Would a 1 or 2 season bag be enough?
 
Thanks…hope this thing gets noticed in the ever-dead Great Outdoors forum!!