The linear and thermal nonlinear spectral responses of silica and hybrid silica/polymer microdisk resonators are investigated. Both types of resonators can be fabricated using the same technological procedure with only slight modification. An extra polymer layer results in opposite sign of the nonlinear thermal optical response of the hybrid microdisks compared to the pure silica ones, which can be explained by the different thermorefractive coefficients of silica and polymer. A full compensation of eigen frequency shift, caused by thermal nonlinearity, has been demonstrated experimentally.