The liners in some running shorts can be too baggy, too tight, or cause chafing. Often, to get the right fit in the outer garment, the inner lining wouldn't fit me. It was frustrating.
So, about 10 years ago, I started cutting out the lining in my running shorts and wearing high tech sports briefs instead... typically, Asics. That way I could get the perfect fit in both pieces of apparel.
Then, I figured that boxer briefs might be warmer in winter because they were longer. I've tried performance boxer briefs from Adidas, RBX, Russell, Reebok, Puma, UnderArmor, Champion, and Hanes... all bought at TJ Maxx at far below retail. Fit is a personal preference so I can't recommend one brand over the other, but I'll point out that some materials were far warmer than others. They are WAY BETTER than regular liners in the winter. Since you can mix and match, you can avoid the dreaded "tights under shorts" look that gets panned here every winter.
Finding boxer briefs that are cool in summer is a challenge. Some brands offer a micro mesh material that is alleged to be cool in the summer. I've tried a few. Reebok's short boxer brief in this material is pretty cool, but not quite as cool as the Asics performance brief I've used for years.
The great thing about this approach is that you can pair up the perfect fit in inner and outer garments. Another plus is that you can also buy linerless shorts for $9.95 to $20 almost anywhere and use them as running shorts.