Ive heard issues of oil pumps acting up/failing due to having to pump thicker oils than specified. I do not have any data for it, so cannot tell if it is a wife's tale or what.
There are some general temperature/viscosity rules, which may vary slightly depending upon engine design, but are probably close enough for one size fits all.
Using 15w-40 oils only above 4F, and using straight 30 weight oils only above 40F (this is actually labeled on the pennzoil HD30 bottle!) come to mind.
Older cars had charts that recommended different oils for different temperatures. I think some (e.g. subaru) still have that to some extent at least.
The real question is why do you think you need to do this, and what end are you trying to have more viscosity? It is pretty well established that for typical use, it is better to have a thinner oil at startup that flows easier. At high temperatures, it may be desireable to have a bit more viscosity at the bearings, but that said, the typical conventional 5w-30 oil may well shear to a 5w-20 spec oil before too long anyhow... 5w-20 oils tend to be pretty robust.