I worked on a big waterflood oil field, where injection water was both drawn from shallow aquifers cnnnected to the sea, and was from cleaned production water.
The latter wasn't yet successful during my time there, but rsearch was continuing then.
The heater to separate oil from water was called a "water knock-out."
I conducted field tests, of "water quality," regarding flow in a porous media.
That was 47 years ago. Both production and injection well drilled directionally from shore and from platforms.
We have "treaters" on just about every well, to break oil/water emulsions and 'treat' the oil for shipment (truck or pipeline), and they, too are heated. So, I'm guessing you were down south or in Cali, if in the states, although Prudhoe is a possibility.
But here, during winter, frac water has to be heated (before the frac) or you get a huge, steel enclosed ice cube with wheels on one end, that might be thawed by next august.
There are a bunch of these (20 or more) on almost every frac job, and all have to be kept from freezing.

In a waterflood, you are injecting water at a constant rate more or less, on a frac job, over a very short time, and then recovering flowback water when the well is initially produced. Different scenarios.
To re-use that water, it would have to be treated, brought back into spec, chemically, and moved and stored, rather than disposed of by injection. the storage during treating the water to bring it back into spec and afterward is a bugaboo, and requires multiple handling of the water, not necessarily when it is ready for use. That means storage, and to do that without chemically altering the water, that means tanks, and those would have to be heated in winter to prevent freezing--all more expensive than disposal and starting with a fresh batch when you need it.
About a mile down, here, far from (vertically) and well isolated (geologically) from surface aquifers, we have a lovely sand formation which accepts incredible amounts of injected water, without seismic problems. It's cheaper that way, and employs people at the disposal depots as well.