We explore the influence of hot background temperatures in stellar clusters on the formation and evolution of photoevaporating disks. The disk forms from the gravitational collapse of a pre-stellar core. For a core with a relatively high temperature (>40 K), the angular momentum of the core is expected to be low. In the core-collapse stage, most of core mass directly falls onto the central star or the disk near the star. External photoevaporation is ineffective in this environment. The viscosity in the disk dominates its evolution, which leads to a high efficiency of the mass and angular momentum transports. The disk properties are determined by the core properties. In the vicinity of massive stars with strong external FUV fields, the disk can still survive when the background temperature is high (similar to 100 K). We suggest that the diversity of the molecular cloud core properties may lead to the diverse properties of the disk photoevaporation in clusters. We also consistently interpret the findings in NGC 1333 that low-mass disks (0.002-0.004M(circle dot)) can exist in such young clusters (1-2 x 10(6) yr) with mild external photoevaporation.