Word for a person that is both caring and cold-hearted logical

I think you're describing someone who is selfless (in a healthy way), in that she really does seek the good of others, but also very rational/logical. I'm not sure there is a word that combines these two different aspects of personality.

Maybe the most encompassing word is a plain one: thoughtful, because it has two fitting definitions:

1. given to careful thought; exhibiting or characterized by careful thought: a thoughtful essay 2. having or showing heed for the well-being or happiness of others and a propensity for anticipating their needs or wishes.

You can call her judicious (having, exercising, or characterized by good judgment; discreet, prudent, balanced, or wise) or circumspect (heedful of circumstances and potential consequences; prudent). But it doesn't quite capture her kindness as does thoughtful.

You could use the word "pragmatic", in the sense that your friend does the logical thing without consideration for its implications - good or bad.

You may be looking for

affectless adj
Having or showing no emotion; unfeeling

[See TheFreeDictionary]

That sounds like a typical description of judges.

The nearest single-word adjective might be "just", which has connotations of both "empathy / fairness", yet "logic taken to an extreme".

Otherwise, you might want to consider using a phrase instead of a single word, e.g. "impartial/rational, yet/and empathetic/caring".

I would say she's paradoxical as the term means to embody what would be two conflicting characteristics in a harmonious unity. Spanish author Marquez points this out.

She's a pragmatic objectivist who doles out her goodwill to others only to benefit her own end: feeling good about herself helping someone else. Read Rand's The Virtue of Selfishness.

The OP's aunt is a person untainted by sentimentality, not one word I'm afraid but there are a couple of references online.

• …philosophical arguments untainted by cheap sentimentality or religious doctrine. Those who cannot be persuaded away by philosophical arguments should probably not be persuaded away at all if their reasons are sound and their motives are worthy

• Hume had an equally detached perspective on Scotland itself. His Scottishness was forward-looking, and untainted by sentimentality about the past. Hume believed in progress to the extent that he was prepared to accept that the modern world was, politically speaking, preferable to the ancient.

• Mr. Minchin's distinctive touch is emotion untainted by sentimentality. The treacle trap was especially hard to avoid considering that “Matilda” and “Groundhog Day” deal with children and redemption — subjects that have been known to trigger maudlin triteness.

• It is a view untainted by sentimentality and edification. Seen in a such a light, social democracy has been distinguished by the following attributes.

I can relate to this because that sounds like me, and I call it "keeping it real" or "keeping it ?" staying true to one's self" or one of my favorite sayings, " I tell it like it is and call it how I see it. Sorry for the slang but out of all the words in the dictionary I think that was the best way to put it. Just because a person makes a honest/ and or realistic statement to someone doesn't make them cold hearted, it can be but it's not if you care about the person's best interest not what they want. I say things that sound pretty cold sometimes but I'm just simply giving my opinion based on evidence and facts, I've gathered over time, even if I care about the person, I'm able to set aside personal feelings, and in some way it seems cold but it isn't because whatever I have to say is simply what is best for that person, You would call that, straight forward, honest, opinionated, caring for a person's best interest at heart.

utilitarian
The word utilitarian was coined by the philosopher and judge Jeremy Bentham, who argued that his principle of utility would create the "greatest happiness for the greatest number of people." The noun form of utilitarian refers to a person who adheres to this philosophy of usefulness.
https://www.vocabulary.com/dictionary/utilitarian

In other words, the person in question gauges their ethical and moral choices based on the perceived total value to all affected. The low utility cost of making soup is greatly outweighed by the benefit of making someone feel better, so it is not even a question, it is clearly the right choice.

A non-utilitarian might simply be too busy, or they might be worried their soup won't taste good, or they assume someone else will do it. These things just don't matter to a utilitarian, it's simply [value gained] - [value lost] = [positive].

Conversely, many people, when seeing a loved one suffer, would gladly take the suffering upon themselves, if possible, to spare the other. This might even be seen as selfless and heroic, but to a utilitarian it is nonsensical as the net outcome would be 0.

In these terms, it is easy to see the rationale behind killing 1 to save 10. Most people would rather "allow" 10 people to die through non-action than actively murder 1 person, but to a utilitarian, 1 life lost is objectively better than 10 lives lost, end of story.

In the end, it has nothing to do with them not caring, or having no emotions or even being "cold". They simply value the greater good above all else.

If this is possible at all - which I tend to think it may not be - then Chymera may best suit. Are you sure that being “altruistic” for her is not part of a calculation where she decides that for the time being it is better to lean towards this pole. If she is making you chicken soup when you are sick, would she poison it if it would save the life of someone she considers superior or that of two or more others? On the other hand, might she “feel” like being calculating is better at times, to either protect herself from the weight of making truly altruistic decisions, or to mimic someone else in an attempt to impress?