Map from Google - Cusco

In Cusco (or Cuzco), the ancient capital of the Inca Empire, located at 3,300 metres above sea level in the Andes, the climate is temperate, spring-like during the day all year round, but with cold nights in the winter period from May to August, when the minimum temperatures are near freezing; on the contrary in summer, from November to March, which is also the rainiest period, night temperatures are milder, around 7/8 °C.
During the day, the temperatures are uniform throughout the year, and reach 20/22 °C when the sky is clear, even in winter, due to the strong heating caused by the mountain sun. Instead, in winter a cool mountain breeze starts to blow at sunset, and in winter nights there may be slight frosts.
During the day, the temperature never reaches 30 °C, even though the tropical mountain sun is very strong and requires appropriate protection.
Here are the average temperatures.
Average temperatures - Cusco
CuscoJanFebMarAprMayJunJulAugSepOctNovDec
CuscoJFMAMJJASOND
Min (°C)776531125667
Max (°C)191919191919192020212120

Rainfall is not abundant, since it amounts to 700 millimetres per year, and is concentrated in the summer months, in particular it's equal to or greater than 100 mm per month from December to March. In these months, showers occur almost daily, although they are often short-lived.
Here is the average precipitation.
Average precipitation - Cusco
CuscoJanFebMarAprMayJunJulAugSepOctNovDecYear
CuscoJFMAMJJASONDY
Prec. (mm)14513510545102510204070125712
Days18131183222781216102

In the winter period, from May to August, it rains very rarely. The rains begin to fall in September, although they are initially rare and brief.
The amount of sunshine in Cuzco is very good in the dry season from May to August, when blue skies prevail, it is still good in the intermediate periods, when the rains are frequent but short-lived, while it becomes mediocre from November to March, due to frequent cloudiness, which can lead to showers.

Cusco

When to go

The best time to visit Cuzco goes from May to October, being the driest and sunniest. Since it is winter, you should be equipped for the cold at night, and be ready to uncover (but at the same time to protect yourself from the sun) during the day, when the air is mild.
In April and September there is some showers, but generally of short duration and not heavy.