  Motivated by the absence of Misner string in the Euclidean Taub-Bolt/NUT
solutions with flat horizons, we present a new treatment for studying the
thermodynamics of these spactimes. This treatment is based on introducing a new
charge, $N=\sigma \, n$ (where $n$ is the nut charge and $\sigma$ is some
constant) and its conjugate thermodynamic potential $\Phi_N$. Upon identifying
one of the spatial coordinates, the boundary of these solutions contains two
annulus-like surfaces in addition to the constant-r surface. For these
solutions, we show that these annuli surfaces receive electric, magnetic and
mass/energy fluxes, therefore, they have nontrivial contributions to these
conserved charges. Calculating these conserved charges we find, $Q_e =
Q^{\infty}_e-2N\Phi_m$, $Q_m =Q^{\infty}_m+2N\Phi_e$ and $\mathfrak{M}
=M-2N\Phi_N$, where $Q^{\infty}_e$, $Q^{\infty}_m$, $M$ are electric charge,
magnetic charge and mass in the $n=0$ case, while $\Phi_e$ and $\Phi_m$ are the
electric and magnetic potentials. The calculated thermodynamic quantities obey
the first law of thermodynamics while the entropy is the area of the horizon.
Furthermore, all these quantities obey Smarr's relation. We show the
consistency of these results through calculating the Hamiltonian and its
variation which reproduces the first law.
