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The Temperature of the Hot reservoir should be increased by 359.86°C

Explanation:

A Carnot engine is a reversible engine, that means that it can work both as a heat engine and as a refrigerator, it can both use heat from a hot reservoir (part of which later must end up in a cold reservoir) to produce work, or use work to move heat from a cod to a hot reservoir.

The efficiency of a carnot engine working as a heat engine is given by:

were and are the Absolute temperatures of the hot and cold reservoir respectively.

To get the absolute temperature in K from the relative temperature in °C, we must add 273.15 K (the absolute temperature of the freezing point of water at atmospheric pressure)

Thus:

Now, if we know the Temperature of the cold reservoir, and the engine's efficiency, we can use that information to get as follows:

Now, that is the Temperature of the hot reservoir to begin with, but if we want a higher efficency, we need to increase until .

To find out what value has to reach, we repeat the same calculation as before, except now

So has increased from   to , that means an increase in temperature of :

This increment of 359.86K is also an increment of 359.86°C, because increments are relative measures of temperature.