Yes, heat energy is produced by the electrons;however small it may be,actually if we consider a resistance then it is an hindered to the flow of electrons,as a result of which the electrons collide with the particles of wire resulting in loss of energy in the form of heat.the equation of heat generated is:
H=(I^2 *R*t)
where-
H=heat produced in joules
R=resistance of the material in ohm
t=time of current flow in seconds
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