It is a frustrating problem because everything is fine 95% of the time, but now and again we get these heat waves which make life difficult for maybe a total of two weeks of the year. The various solutions all involve a considerable expense and a lot of labour, and the thick insulation between the beams would alter the character of the place. All this just to solve a short-term discomfort in summer.
If your situation is adequate 95% of the time, then I'd think the appropriate answer would be to get a larger window unit. There's no way any of the recommendations I offered would be cost effective.