We study the phase behavior of associating dendrimers in explicit solvents using classical density functional theory. The existence of association enables uptake of solvent inside the dendrimer even for unfavorable Lennard-Jones interaction between the solvent and dendrimer. Depending on the distributions of associating sites, the dendrimer conformation can be either dense-core or dense-shell. The conformation of the associating dendrimer is greatly affected by the temperature. Due to the interplay between association interaction and Lennard-Jones attractions, we find the lower critical solution temperature (LCST) behavior of dendrimer conformation and study how it changes as the dendrimer size or solvent size changes. The dendrimer in our study displays no LCST behavior at low generations, and it has a maximum LCST at G4. Moreover, increasing the solvent chain length decreases the LCST. For solvents with self-association, the competition between solvent-solvent association and solvent-dendrimer association also tends to reduce the LCST. Qualitatively consistent with experiments, our results provide insight into the molecular mechanism of the LCST behavior of associating dendrimers.