My baby is fed on expressed breast milk so when I take her out, I usually bring a cold bottle in an insulated bag (it is meant to keep the bottle cold for 3 or 4 hours) and then heat it up in a bowl of hot water when needed. I've never had any problems with my little one and the milk.
In relation to defrosting in the diaper bag, my lactation consultant recommends against "slow" defrosting and suggests that I quickly defrost frozen milk in hot water at home and then refrigerate it, so I've always done that. However, she didn't explain why so it may be okay to just let it thaw out, as Erina320 suggests.