  We study the phase transition behavior of a frustrated Heisenberg model on a
stacked triangular lattice by Monte Carlo simulations. The model has three
types of interactions: the ferromagnetic nearest-neighbor interaction $J_1$ and
antiferromagnetic third nearest-neighbor interaction $J_3$ in each triangular
layer and the ferromagnetic interlayer interaction $J_\perp$. Frustration comes
from the intralayer interactions $J_1$ and $J_3$. We focus on the case that the
order parameter space is SO(3)$\times C_3$. We find that the model exhibits a
first-order phase transition with breaking of the SO(3) and $C_3$ symmetries at
finite temperature. We also discover that the transition temperature increases
but the latent heat decreases as $J_\perp/J_1$ increases, which is opposite to
the behavior observed in typical unfrustrated three-dimensional systems.
