15W-40 is probably OK for those temperatures. However, if the engine has less then perfect compression or the valves need adjustment or the starter is not perfect, then you will get some starting problems. In such a case, it's time to switch to 10W-40.

Or, switch to synthetic and then you don't need to be as cognizant of the thickness of the oil. You can go 5K on synthetic. It's a bit more costly, but, not significantly, when you take the filter into account.