【Temerity】 , 【audacity】 ,  【hardihood】 ,  【effrontery】 ,  【nerve】 ,  【cheek】 ,  【gall】  are comparable when they mean conspicuous or flagrant boldness (as in speech, behavior, or action).

【Temerity】 usually implies contempt of danger and consequent rashness; often it suggests, especially when a proposal or project is under discussion, a failure to estimate one's chances of success.

【Audacity】 implies either a bold and open disregard of the restraints imposed by prudence, convention, decorum, or authority or undue presumption in making advances.

【Hardihood】  stresses firmness of purpose and often additionally implies considered defiance (as of conventions or decorum). It may be used without depreciative intent, but it is frequently employed as a term of contempt almost equivalent to insolence or impudence .

【Effrontery】 is definitely derogatory; it is used in place of any of the three preceding words when one wishes to impute flagrant disregard of the laws of courtesy, propriety, or fair dealing or an arrogant assumption of a privilege.

【Nerve】  ,  【cheek】  , and  【gall】  are close to  【effrontery】  ,  【nerve】  , however, often carrying a strong suggestion of 【hardihood】 ,  【cheek】  of impudent self-assurance, and  【gall】 of outrageous insolence.