How can I get a measure of the semantic similarity of words?
Word2vec does not capture similarity based on antonyms and synonyms. Word2vec would give a higher similarity if the two words have the similar context. Eg
The weather in California was _____ .
The blank could be filled by both hot and cold hence the similarity would be higher. This concept is called Paradigmatic relations.
If you are interested to capture relations such as hypernyms, hyponyms, synonyms, antonym you would have to use any wordnet based similarity measure. There are many similarity measures based on wordnet. You may check this link