Map from Google - Santiago_de_Compostela

The climate of Santiago de Compostela, capital of Galicia, located in the northwest of Spain, and pilgrimage destination, is cool and moist, being strongly influenced by the Atlantic Ocean. The average temperature of January and February is 8.5 °C, that of July and August is 19 °C.
Here are the average temperatures.
Average temperatures - Santiago de C
Santiago de CJanFebMarAprMayJunJulAugSepOctNovDec
Santiago de CJFMAMJJASOND
Min (°C)55679121414131076
Max (°C)121214161821242422191512

Rainfall is abundant, and amounts to 1,900 millimetres per year; it reaches or exceeds 200 millimetres per month from November to February; the rains are also frequent, at least from October to May, when it rains for at least 13 days a month; the only relatively dry season is the summer, especially in July and August, when it rains "only" for 5 days per month.
Here is the average precipitation.
Average precipitation - Santiago de C
Santiago de CJanFebMarAprMayJunJulAugSepOctNovDecYear
Santiago de CJFMAMJJASONDY
Prec. (mm)2602251451401458040551251952002801890
Days16141314148559131416141

The wind blows frequently, and can be strong especially between October and April.
Fog is another feature of this climate: it can form all year round, when there is no wind, even on summer nights.

Winter, from December to February, is quite mild, but it is also cloudy, rainy and windy. The wind increases the feeling of cold. Very cold days are rare: at most the temperature drops at night around freezing or a few degrees below. Snow is very rare, and even when it falls, usually there are not large accumulations.

Spring, from March to May, is cool, humid and rainy. Atlantic weather fronts pass regularly, and the wind blows frequently. At night it can get cold even in May. But over the weeks, especially from mid-April, the first mild and sunny days occur, thanks to the Azores Anticyclone.

Summer, from June to August, is sunny or pleasantly warm during the day, and cool at night. Fog often forms at night and in the early morning. Sometimes at night it can get quite cool even in summer, since the temperature can drop below 10 °C. Every now and then, there may be hot days, with highs around 35 °C. The passage of some Atlantic disturbances cannot be excluded, with a bit of cool and rainy weather, but this occurs less frequently than in the other seasons.

Autumn, from September to November, is cool, humid and rainy. In September, especially in the first part, there are still many sunny days, with an almost summer-like weather. Sometimes this happens even in early October.

The amount of sunshine in Santiago de Compostela is good in summer, when fine weather predominates, while in the other seasons, and especially in late autumn and winter, the sky is often cloudy.

Cathedral of Santiago de Compostela

The sea, along the northwest coast of Spain, therefore near Santiago de Compostela, is a bit cold even in summer, as you can see in the following table, regarding the sea temperature at La Coruña.
Sea temperature - La Coruna
La CorunaJanFebMarAprMayJunJulAugSepOctNovDec
La CorunaJFMAMJJASOND
Sea (°C)131313131416181918171514

When to go

The best time to visit Santiago de Compostela is summer, from June to August or the first half of September, being the most dry and sunny. July and August are the warmest and least rainy months. Even in midsummer some rain must be put into account, and some nights a little cold. Those who suffer from the heat, to avoid the albeit rare hot days, can choose May (especially the second half), June and September (especially the first half), knowing, however, that it could rain more frequently.