B&M tranny cooler install

Just purchased a B&M transmission cooler and it seems that the hose that was sent with it was a size smaller than 3/8 and I think the transmission in my 2001 xj is exactly 3/8. I purchased 3/8 double barb fittings to connect the transmission cooler hose to the existing hose, but the fitting is a tight fit with the smaller hose sent with the cooler. The cooler is the same model as the one used in this post ... http://www.jeepin.com/features/trannycooler/

Does anyone know if using this smaller hose size and cooler could result in a leak or other problem?

Any ideas?

Try finding some 3/8" power steering hose. NAPA or your better parts places will have it in bulk. Just get about 5 feet of it.

It's what I'm using on my trans cooler, and what I've seen others suggest using.

It will work fine, it is what I have on mine