My answer is based on four things; generalizations about design, use, state of tune and environment are the inputs I'd consider here.
- presuming the vehicle/equipment doesn't inherently have an OEM design flaw that predisposes it to accelerated wear
- assuming the use factors of the vehicle/equipment are typical of the design intent and not abusive or akin to neglect
- considering the vehicle/equipment is not modified in a manner which would escalate wear (heavy mechanical or electronic perf mods, etc)
- using a grade of oil that is generally acceptable by the OEM for the application
UOA wear data analysis has shown that a move from one grade to another (either up or down) does not significantly shift wear in a matter that we'd be able to discern. Engines that are spec'd for a 30 grade can safely go up to a 40 grade or down to a 20 grade and not see any major concerns.
There are some engines I've seen in particular that truly could not care less about what grade of oil is in the crankcase, as long as it's a proper spec for the application; their wear rates don't seem to budge much no matter what grade you use (Ford 2v mod motors; GM 6.6L Dmax, etc). Other engines are somewhat finicky, or have a design issue that causes concern (Chrysler 5.7L Hemi engines and their propensity to eat cams; oil isn't the cause, but it also can't seem to stop the problem).
It's important to use a lube spec'd for the type equipment. Don't use a GL-5 gear oil in your engine, for example. Make sure you use the right category of lube hierarchy (don't use a CF where CJ-4 is called for; don't use SG where SN is called for).
The caution would come from when you might alter one or more of the boundary conditions I set forth. I've seen data that indicates some things could go awry, especially if you combine any of those categories. Example: you have a "tuned" engine, use it for racing, and don't consider the elevated operating temps. Or, you live in a super-cold area where it's routine to see -15F starting temps, but use a 15w-40 diesel lube in your engine spec'd for 0w-20.
The data I've processed shows that "generally" moving up/down one grade isn't a big deal at all. It typically won't help or hinder the wear rates, IF the other conditions are not undesirable.
To the OPs question ... going from a 0w-20 to a 15w-50 MIGHT have an effect, or may not, depending upon those other conditions I speak of. He did put a boundary on the ambient temps, but didn't address the specific engine series, the expected use factors, the lube spec, etc.