  We study a Langevin-like model which describes an inertial particle in a
one-dimensional harmonic potential and subjected to two heat baths and one
athermal environment. The thermal noises are white and Gaussian, and the
temperatures of heat reservoirs are different. The athermal medium act through
an external non-Gaussian noise of Poisson type. We calculate exactly the
time-dependent cumulant-generating function of position and velocity of the
particle, as well as an expression of this generating function for stationary
states. We discuss the long-time behavior of first cumulants of the energy
injected by the athermal reservoir and the heat exchanged with thermal baths.
In particular, we find that the covariance of stochastic heat due to distinct
thermal baths exhibits a complex dependence on properties of athermal noise.
