  In a recent paper published in this Journal, Khordad and collaborators [J Low
Temp Phys (2018) 190:200] have studied the thermodynamics properties of a GaAs
double ring-shaped quantum dot under external magnetic and electric fields. In
that meritorious research the energy of system was obtained by solving the
Schr\"{o}dinger equation. The radial equation was mapped into a confluent
hypergeometric differential equation and the differential equation associated
to $z$ coordinate was mapped into a biconfluent Heun differential equation. In
this paper, it is pointed out a misleading treatment on the solution of the
biconfluent Heun equation. It is shown that the energy $E_{z}$ can not be
labeled with $n_{z}$ and this fact jeopardizes the results of this system. We
calculate the partition function with the correct energy spectrum and
recalculate the specific heat and entropy as a function of low and high
temperatures.
