I was saying at a convention this weekend that whenever a reader complains to me about one of my characters acting "too modern", the thing they're complaining about is almost invariably something I took almost verbatim from a period letter, diary or account.
I think that many of our ideas about what is "modern" are themselves the product of constructed history. The problem I have as a novelist is less that readers expect the characters to be like them, and more that readers expect the characters to be like other historical stories.
Some of the narratives we have about modernity (using that term colloquially) are very deliberate 19th and 20th century constructions -- for example, many ideas about women's occupations in the past. So we're dismantling those things all the time.
Also, the differences among humans of a given time can be as vast as the average difference between two humans of different points in time. So our ideas about "how a person thinks" need to be really flexible.
Of course it's true that you can't just transplant a character, ideas and all, to any century you want (well you can, but it will not be very convincing IMO). I think it always makes sense to begin with an open mind and with whatever records we have from that time.
Postscript: If you're interested in human patterns of seeing their own time and the past, @paulisci has a book coming out: