Let $v$ denote the speed of sound in a fixed solid, at a fixed temperature $T$. This will depend on properties of the solid (such as the bulk modulus and density).
Given an increase in $T$, does $v$ necessarily increase?
For calculation purposes, we should assume a "small" change in temperature. For an ideal gas, $v$ increases as the square root of $T$, so perhaps the same is true in the limit of compressing the gas into a solid.
In solids, I came up with two opposing naive/vague thoughts:
1) If there is an "index of refraction" for sound in materials, then I would expect an increase in $T$ to decrease this index, hence increasing $v$.
2) If I can view the propagation of sound in terms of a coherent collection of phonons, I would expect an increase in $T$ to hurt this coherency, hence decreasing $v$.
Edit: To clarify, I am searching for a theoretical explanation.