In warm weather, you can run the 15w40 no problems. As it gets colder, the 5w40 will work OK.
I used to run the 5w40 Rotella year around in my '88 Cherokee with the 4.0. I stopped when: I grew tired of keeping a special stock of oil for just the Jeep (tried Rotella in my F150 and stopped after a year when my fuel mileage was substantially lower - over 5%, but never noticed the same effect in the Jeep), and the oil pressure was high in the dead of winter, and stayed that way for a very long time. Basically the guage would end up just over 60 psi, and stay there in cold weather. Regular function is 60 psi at startup cold, then dropping a bit to 50-55 psi (depending on the weight) at power, 25 psi at idle. Its been that way since new.
5w40 worked fine and UOA's showed wear was about the same between a year around 5w40 regimen versus the 5w30 winter/10w30 summer that I have returned to.