  We consider the scenario of thermal transport through two types of Andreev
quantum dots which are coupled to two leads, belonging to the Class D and Class
C symmetry classes. Using the random matrix description we derive the joint
probability density function (j.p.d.f.) in term of Hypergeometric Function of
Matrix Arguments when we consider one lead to be attached ideally and one lead
non ideally. For the class C ensemble we derive a more explicit representation
of the j.p.d.f. which results in a new type of random matrix model.
