Here's the thing...
It's summer and it's hot. I wear padded lycra under my shorts / pants the rest of the year, but it's just way too hot to do that now. I really try to not ride in just cycling shorts / jersey unless I'm putting in some serious miles. (I try to not be THAT guy wearing a full kit on a 7 mile commute to work.)
That being said, what do you guys wear under your casual shorts? I've just been wearing [tighter-fitting] briefs to keep my junk in place. I'm on a B-17, so I don't really need padding for a 14 mile round trip. My priorities are to keep cool and keep my stuff in place.