This work deals with chaotic quantum dot connected to two and four leads. We use standard diagrammatic procedure to integrate on the unitary group, to study the main term in the semiclassical expansion of the noise in the three pure Wigner-Dyson ensembles at finite frequency and temperature, in the noninteracting and interacting regimes. We investigate several limits, related to the temperature and the potential difference in the leads, in the presence of a capacitive environment. At the thermal crossover regime, we obtain general expressions described in terms of parameters that can be controlled experimentally. As an interesting result, we show the appearance of asymmetries in the noise, controlled by the topology of the cavity and the number of open channels in the corresponding terminals.