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Hello and welcome to JustAnswer.
My name is Vlad.
I have seen exactly the same problem a few times before and it was caused by partially clogged heater core.
It is hard to believe but a side tank of the heater core usually gets clogged causing coolant to circulate only through some section of the core and that is why only one side is warm. You can try to flush back flush the heater core but it does not always help. It really depends on how solid contamination inside the core.
I am just checking if my answer has helped or you need more assistance?