Hi,
I would recommend you :
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Hyde, Jekyll, Me : I didn't rate it high (only 6.5/10) but it aired at the same time as Kill Me Heal Me (10/10 for me so...) so the contrast was far too great. Maybe you'll enjoy it more watching it now. The man has a DID (only two personalities) with his main personality being the cold one while the other is very friendly. The problem is the woman think of him as two brothers and falls in love with the friendly one... In a way, it is interesting and you might like it but, as for me, I had to fastforward some boring scenes.
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Nine : nine times time travel : (8/10) It's
not a saeguk despite its name, just a regular but very interesting time-travel drama in modern time only ;)
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Who are you :
(10/10) Not the one you watched. This one is from 2013. This one is about a policewoman seeing ghosts after a 6 years coma. In this drama, the woman can be considered the cold person oppening up to the man.
Apart from those three, you already watched the ones I could have recommanded. Enjoy !