  The divergence of the string partition function due to the exponential growth
of states is a well-understood issue in flat spacetime. It can be interpreted
as the appearance of tachyon modes above a certain temperature, known as the
Hagedorn temperature $T_H$. In the literature, one can find some intuitions
about its generalization to curved spacetimes, where computations are extremely
hard and explicit results cannot be provided in general. In this paper, we
present a genus-zero estimate of $T_H$, at leading order in $\alpha'$, for
string theories on curved backgrounds holographically dual to confining gauge
theories. This is a particularly interesting case, since the holographic
correspondence equates $T_H$ with the Hagedorn temperature of the dual gauge
theories. For concreteness we focus on Type IIA string theory on a well known
background dual to an $SU(N)$ Yang-Mills theory. The resulting Hagedorn
temperature turns out to be proportional to the square root of the Yang-Mills
confining string tension. The related coefficient, which at leading order is
analytically determined, is the same as the one for Type II theories in flat
space. While the calculation is performed in a specific model, the result
applies in full generality to confining gauge theories with a top-down
holographic dual.
