In several articles I've found about it, climate change is only but one factor among several other which have contributed to the boom of jellyfish population. The increase of the jellyfish population, however, has been acknowledged in several places of the world, and it seems to be a global trend.
Jellyfish are booming because of:
- Lack of predators due to overfishing.
- Overabundance of nutrients due to fertilizers being dumped into the sea as sewage waters.
- Warmer waters due to global warming.
Just point 3 is linked to climatic change, although it remains an important factor.
EDIT: I know this is old, but I've found some sources which paint a much better and more accurate response. The relationship between climate change and increasing population, or frequency of washup on the beaches, of jellyfish is currently under investigation:
In 2012, a task force of international jellyfish experts evaluated the scientific evidence behind the theory that jellyfish blooms were increasing as a result of global temperature changes. What they found, first and foremost, was a lack of information. Jellyfish are notoriously difficult to study, blooming unexpectedly in inaccessible corners of the sea. The data that were available suggested a more complicated story, in which jellyfish blooms occur in waves that coincide with natural fluctuations in the environment. While there was a slight upward trend of blooms in recent years, that increase was within the normal range of variability. The group didn’t reject the jellyfish-climate link, but they suggested that there might be other explanations for the increase in jellyfish abundance.(1)
If you are interested, the alternative explanations were mostly anthropogenic as well, mainly overfishing and destruction of maritime wildlife and biomes and contamination due to gray waters.
On the issue on why they end washing up the beaches, it's all in the currents and streams of the oceans, and there's a novel study which aims to predict the probability of jellyfish on spanish shores thanks to a metereological study of several athmospheric indexes (source in spanish).