Usually I would try to put this in terms of cognitive functions, but I don't know how well-versed you are, so let's do it the wordy and possibly incomplete way.
Putting emotions aside is a pretty normal thing for all people. We all have them and we have to learn to deal with them, one way or another. What distinguishes us from one another are the ways we deal with them and the consequences of our choices can leave imprints on how we develop.
For INFJs, there are different stages of pushing away emotions or embracing them. Some of us think that we feel too much, push it aside, let it bottle up, are easily overwhelmed. Our personal emotions and ethics are countervalued, put simply. Some of us have pushed our emotions so far down that we hardly feel anything anymore - I guess this is what you experience as a certain coldness. I know it can get worse than that, but unless it comes up I won't talk about it here. It is quite natural for us to be empathic, although this empathy is more of a myth than an INFJ-exclusive "psychic" ability. More to the point, we understand different perspectives and therefore have an easier time tapping into the emotional world of others. For anything more, it depends on belief and individual experience. There are INFJs who are theoretically completely non-empathic or controlled in their emotional output, there are countless varieties, stemming from countless possible defense mechanisms.
I have learnt that swimming against the current rarely acheives anything. You're more likely to lose control (which you never really had for lack of dealing) and sort of... explode. We don't have it as easy as other types that don't value the expression of emotion at such a high rate or intensity (I have a theory that we only value to express it because we partially gain energy from taking it in). However, letting everything out unfiltered can become too much very fast. We need to find a balance where we let ourselves feel what we feel without necessarily expressing it at once (perhaps expressing it through journaling), so we are not overwhelmed ourselves or bottle it up. Before we can begin to perceive or judge the world, we have to start with ourselves, see ourselves for who we are and make our peace with it. In some sense, that way we are forgiving ourselves for who we were in the past, the clay that has moulded us into who we are now, in the moment of acknowledgement. It's not something you can decide so easily and move on, unfortunately. It is a decision that has to be made each day, until we unconsciously incorporate it into our behaviour, the same way that the defense mechanism first took hold. Unless it's already part of your nature, it feels odd and contrary at first, but it gets easier with time.
I feel very intensely, tiny nuances from the different kinds of love to a hatred so pure it feels like you're forever lost to darkness, from the hottest flame to an icy, coldly burning nothingness. I have learnt to temper it, to some degree, by allowing it for as long as I need it. My emotions have flow (I don't know how it is with you), and it doesn't do me good to hold on to a feeling that is ready to pass once felt to completion. Of course, emotions can be steady as they can be fleeting - also part of the flow. I used to be in the clutches of my own emotions, mostly negative ones such as anger, envy or hatred, until I learnt that by holding on to them they were all merely a defense from being hurt again. They hardened me to the world, made me impervious to the frequencies that surrounded me. It feels like a miracle now that I was able to get out of that. It took me years to understand what I knew already. The peace of flow, that all has its time, even emotions.
This is not all. There is the part where you don't just have to let in positive frequencies and generate them yourself, but you learn to see that you need to divorce yourself from certain influences if you cannot withstand them. It is a temporary way of keeping the peace, if an effective one. Sooner or later you have to face the music and this will be the ultimate test. Let yourself be ruled by your emotions or feel what you need to accept it and let it go as it arises. And then, it becomes all just a matter of perspective: shifting perspective so that a negative emotion arising out of a negative situation can be disarmed and turned into something neutral or even positive, enabling you to react with kindness in the face of anger and frustration. And before you come to think of the phrase "killing with kindness": real kindness isn't used as a weapon, or it isn't kindness - it's mistaking cruelty for kindness. However, even if you are kind, it may not feel like that to the other party: to them, it may feel cruel, disingenuous and calculated. But the important thing is that you feel the difference.
