Clusters of gold nanoparticles can be used as optically driven stoves to locally heat biological material such as DNA in biosensors or cancerous tissue in thermotherapy. Clusters of gold nanoparticles behave distinctively different from single nanoheaters as they accumulate heat in-between the individual nanoparticles. However, in very large clusters the rear nanoparticles are shed by front-lying nanoparticles such that the optothermal heating saturates with increasing cluster size. We focus on these two effects and describe the temporal and spatial development of heat generation and subsequent cooling of nanoparticle clusters excited by nanosecond laser pulses. It is found that (i) heat accumulation is most important for DNA melting assays to generate enough heat for DNA melting, (ii) shadowing effects are significant in micrometer sized nanoparticle clusters, and (iii) that DNA needs to be heated substantially above the equilibrium thermodynamic melting temperature in order to induce DNA melting by nano...