For the Carnot heat engine, if the temperature of the hot reservoir...

The efficiency of a Carnot engine is given by the formula:

$\eta = 1 - \dfrac{T_C}{T_H}$

where $T_C$ is the temperature of the cold reservoir and $T_H$ is the temperature of the hot reservoir.

When the temperature of the hot reservoir $T_H$ is increased, the ratio $\dfrac{T_C}{T_H}$ decreases.

As a result, the value of $1 - \dfrac{T_C}{T_H}$ increases, which means the efficiency of the Carnot engine increases.

Answer: increases.