Transformer heat losses
... is Eddy current loss a heat loss?

Yes, it is.
Since the eddy currents flow &quot;through&quot; the core itself, the eddy current loss is still a kind of I2R loss (where I is the eddy current and R is the resistance of the eddy currents' return path). Thus, the eddy current loss produces heat and increases the temperature of the transformer.
For the iron core transformers, the core is made up of thin iron sheets (i.e. laminations) insulated among themselves, instead of a solid iron block. This method decreases the eddy currents, and thus the eddy current losses.