Was Star Trek's Captain James Kirk based upon British explorer Captain James Cook?

I had read of a talk show in America, on which a guest spoke of a string of similarities between Captain Cook and the character of James T. Kirk.

I appreciate that parallels can be drawn between many unrelated topics if you look hard enough, but I thought there might be some dedicated Trekkies out there who could support or explode the theory.

Both men had the first name James and similar surnames and were brought up on farms (Cook in Yorkshire, Kirk in Iowa). They both became captains of ships with similar names (Endeavour and Enterprise). Cook's journal said he had travelled "further than any man had ever been before" while Kirk said his mission was "to boldly go where no man has gone before".
Cook and Kirk both set out to describe, rather than conquer or convert the lands they discovered. Cook set out in jolly boats with his naturalist, a surgeon and musket-toting red-jacketed marines. Kirk beamed down to planets with his science officer Mr Spock, his medical offcer Dr "Bones" McCoy and various expendable characters in red jerseys.

The similarities are surely a bit strong to be total coincidence?