Cucumbers are one of my favorite summer vegetables.
According to the Online Etymology Dictionary, Cool here means imperturbable rather than having a low temperature. Being calm and composed, self-possessed in a stressful situation.
The phrase ‘cool as a cucumber’ (c.1732) embodies ancient folk knowledge that was confirmed by science in 1970. The inside of a field cucumber on a warm day is 20 degrees cooler than the air temperature.
The phrase was first recorded in John Gay's Poems, New Song on New Similies, 1732: "I ... cool as a cucumber could see the rest of womankind." http://www.phrases.org.uk/meanings/38500...
The term “cool as a cucumber” is actually derived from the cucumber’s ability to cool the temperature of the blood. Also when applied topically, cucumber really does cool the blood and eases facial swelling, which is why cucumbers are so popular in facial regimens. This information came from http://www.thetowndish.com/2013/07/15/10-facts-you-didnt-know-about-cucumbers/