  Thermodynamic quantities, like heat, entropy, or work, are random variables,
in stochastic systems. Here, we investigate the statistics of the heat
exchanged by a Brownian particle subjected to a logarithm-harmonic potential.
We derive analytically the characteristic function and its moments for the
heat. Through numerical integration, and numerical simulation, we calculate the
probability distribution as well, characterizing fully the statistical behavior
of the heat. The results are also investigated in the asymptotic limit, where
we encounter the characteristic function in terms of hypergeometric functions.

Statistical Mechanics