In a microscopic classic picture, ohmic heating occurs due to collisions. Let's start with the simplest case: a cooper wire and a battery that induces a current. Electrons start flowing and the energy gained by the field that is accelerating them is lost through collisions with the cooper atoms. I think we all agree that the energy transfer to the Cu atoms through these collisions is what makes the wire heats up.
Now suppose we have a plasma, namely a fusion plasma in a magnetic confinement device. It is well known that because the plasma resitivity goes with $T_e^{-3/2}$, then ohmic heating is not really efficient to heat the plasma up to the desired temperature. I have two questions regarding this:
2a) I suppose plasma current is mainly carried by electrons which are much more mobile. Then, it is the electrons that are being accelerated by the field. They make (coulomb) collisions with the ions, so ions will gain energy and increase their temperature. Because these electrons are, in the overall process, not gaining any energy, shouldn't their temperature stay the same? Why is it that $T_e$ also increases?
2b) Why is it said that ohmic heating is a loss process when one makes the plasma energy balance? Because all the energy that is being given to the elctrons in the current by the field stays in the plasma because electrons transfer their energy to the ions and ultimately also to other electrons with whom they can also collide.
EDIT: I realized that my second question (2b) didn't make sense: I was making confusion with something else (see comments below). The first question is perfectly answered by @honeste_vivere