Using path integrals, we derive an exact expression-valid at all times t -for the distribution P (Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P (Q,t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t→∞ exactly recovers the heat distribution function obtained recently by Imparato [Phys. Rev. E 76, 050101(R) (2007)]10.1103/PhysRevE.76.050101 from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen [Phys. Rev. E 69, 056121 (2004)]10.1103/PhysRevE.69.056121; however, this calculation does not provide an expression for P (Q,t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P (Q,t) for the case v=0. © 2010 The American Physical Society.