Pedroia's .356 June, .350 July, and .374 August is pretty tough to beat in this era (obviously guys like Ted Williams, Tony Gwynn, Rod Carew, Paul Molitor etc would have to have better streaks while having seasonal averages higher than Pedroia's monthly averages).
From personal knowledge, I know Mauer and Morneau had some crazy steaks in 2006. That year, Mauer went .319 in April, .386 in May, .452 in June, and as a catcher, I put this 3 month streak well ahead of Pedroia's current 3 month hot streak. Also that year, Morneau went .364 in June (10 HR, 29 RBI), .410 in July (8, 23), .294 in August (4, 22), and brought it back up with .348 in September (2, 19)... those averages, included with his power numbers, I might put that 4 month stretch ahead of Pedroia's as well. That stretch propelled Morneau to the MVP award... will Pedroia's do the same?