What is the significance of the line in Othello in Act V scene ii " Cold, cold, my girl, Even like thy chastity."?

Earlier in the play (Act 3, scene 4) , when Othello asks
for Desdemona's hand, he takes it and says,

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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.