What is the significance of the line in Othello in Act V scene ii " Cold, cold, my girl, Even like thy chastity."?
Given when it is spoken and what transpires as a result, the line is very significant. The notion of Othello's jealousy as a fire spinning out of control, consuming everything in its path can be contrasted with the "cold" demeanor he ascribes to Desdemona. It's an interesting line because Othello is suggesting that Desdemona was cold and detached from Othello. I think it's significant for a couple of reasons. The first is the aforementioned hot rage of jealousy that is running amok in Othello's heart. To contrast Desdemona as cold in this light is another contrasting element brought out between both of them. Additionally, the implication of Desdemona's "cold" manner is that she was the opposite with Cassio, according to Iago's insinuations and Othello's beliefs. In the end, it is this image- the one of a cold and frigid Desdemona contrasted with the intensity of passion Othello imagines with Cassio- that drives him to smother her with the pillow. One can almost imagine the vision in Othello's mind of Desdemona being carnally passionate with Cassio right before he proceeds to smother her. In contrast with the Othello we see at the start of the play as confident, strong, and independent, this character is quite the opposite and the line spoken about Desdemona's cold chastity might have been the last straw to reveal him as such.
Earlier in the play (Act 3, scene 4) , when Othello asks for Desdemona's hand, he takes it and says,
Hot, hot, and moist--this hand of yours requires
A sequester from liberty, fasting and prayer . . .
In this quotation, Othello equates Desdemona's supposed licentious behavior with Cassio to heat and fire. Her hand is a "young and sweating devil." Heat is a metaphor for sexual incontinence, infidelity in marriage, looseness.
Here in Act 5, though, Othello touches Desdemona's literally cold body. He realizes that Desdemona was not a promiscuous woman, that she was always true to him and thus her coldness is a metaphor for her purity. Othello is praising Desdemona; I don't think he believes that she was frigid, or sexually unresponsive to him, as coldness commonly means today.
In Hamlet, Shakespeare also equates chastity or faithfulness to coldness when Hamlet tells Ophelia that "were she as chaste as ice" she would not escape calumny.