We propose two models for the creation of stable dissipative solitons in optical media with the chi((2)) (quadratic) nonlinearity. To compensate spatially uniform loss in both the fundamental-frequency (FF) and second-harmonic (SH) components of the system, a strongly localized "hot spot" carrying the linear gain is added, acting either on the FF or on the SH component. In both systems, we use numerical methods to find families of dissipative chi((2)) solitons pinned to the "hot spot". The shape of the existence and stability domains may be rather complex. An existence boundary for the solitons, which corresponds to the guided mode in the linearized version of the systems, is obtained in an analytical form. The solitons demonstrate noteworthy features, such as spontaneous symmetry breaking (of spatially symmetric solitons) and bistability.
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