The Noam Elimelech (Parashath Tazria) explains it like so: The desire for evil burns hot within us. It is that heat and passion with which we must love HaShem. With the very same fire that burns inside us to do evil, we must burn in desire of HaShem. As long as we don't accomplish this, our love of HaShem is incomplete, since we (chas v'shalom) lust for something else more strongly than we lust for HaShem.
I think there's a subtle distinction here, but perhaps I'm splitting hairs. There is a prohibition against bringing a foreign fire, aish zara, as an offering to HaShem. Wouldn't one normally think that the same fire that burns in the yetzer hara to do evil would be considered such a foreign fire? It seems strange that we would be permitted, even encouraged to serve HaShem with this foreign fire.
There are two points of explanation: The first is that here the Noam Elimelech seems to say that we are supposed to love HaShem with an equivalent heat, not necesarily with the very same heat of the yetzer hara, it seems like he focuses on the magnitude of our love and not the point of origin of that love. In fact he goes on to explain that as long as one's service of HaShem still involves the smallest bit of heat from the yetzer hara, ie. he is not doing the mitzwah entirely l'shmah, then he hasn't really begun his avodah. Case in point, it seems like we are meant to entirely extinguish the flame of the yetzer hara while simultaneously kindling an equivalent flame sourced in the yetzer tov.
This leads to the second related explanation: There is an idea in halachah that when a vessel moves from the reshut, the possession, of unholiness to the reshut of holiness, then it should be passed through water. In other situations where a vessel has been exposed to and infused with forebidden compounds the vessel must be purified through fire.
We see both things happening here. Love is normally associated with water, as rain that falls from heaven to earth demonstrates God's unconditional love for us. Our great love for HaShem is meant to extinguish the yetzer hara, and by suffusing it with love, water, we enable its transfer from a reshut of unholiness to a reshut of holiness. At the same time, the yetzer tov, which was exposed to the yetzer hara through all of our failings, is heated up with the same intensity of fire with which the yetzer hara formally burned. In this way the yetzer tov is returned to its state of purity.
The end result is that we have a yetzer hara which has been brought over to the reshut of holiness and a purified yetzer tov, we are now ready to serve HaShem with both of our yetzers exactly like Chazal originally instructed us.