I am not sure what those effects may be and not sure what kind of changes will be to the weather pattern. If there is a claim that small warm-blooded vertebrates are affected, then it may have something to do with the fact that small objects have proportionally larger surface to volume ratios.
Since heat transfer to and from the environment is proportional to body surface area it means that a change in the weather pattern makes these warm-blooded vertebrates more vulnerable to the changes. If the climate gets warmer, then the small endotherms will lose heat less readily to the environment, and they can also suffer heat strokes more easily. To cope, they may have to evolve to be even smaller, or with less insulation or they may need to become more elongated (since elongated objects have more body surface than round ones). Also if bats or rodents hibernate, and the winters become warmer, that means they would have more trouble because their body cannot become cool enough and their metabolic rates will increase. It means they may starve to death before winter is over unless they have more fat stored in their bodies before they hibernate.