I wear a pair of merino/poly blend long-johns gasp under my bike shorts when it's freezing cold out. They're not bulky, they don't seem to contribute to any problems for me, and as a base layer they're fine for wicking moisture and retaining warmth. Those, my bibs, and a pair of Novara rain/wind pants and I'm usually fine down to the low 30s.

If you're really really freezing down there and want to solve the issue, take your shorts to a tailor who'll work on sportswear. Unstitch the front of the padding and have 'em stitch a layer of tyvek between the padding and the lycra. Your junk might crinkle a bit when you walk around, but you'll be windproof and increase your R-value.