Try a google search on the subject. I've found a few articles stating large handling differences with just small changes in profile. You might never notice the difference, but it wouldn't hurt to know what you are in for.
Another point though, is tire mass. You'll have less mass to absorb the heat (and less surface area to transfer it away) if you run a smaller sidewall tire. If you are running a heavy motorcycle with a load on rough roads, then good heat shedding ability might be noticed. It would be noticed in longevity of the tire and handling characteristics as the tire ages and experiences deeper heat cycles. Again, it probably wouldn't make too much of a difference, but it wouldn't hurt to know.