  The dissipation of intense crustal electric currents produces high Joule
heating rates in cooling neutron stars. Here it is shown that Joule heating can
counterbalance fast cooling, making it difficult to infer the presence of
hyperons (which accelerate cooling) from measurements of the observed thermal
luminosity $L_\gamma$. Models with and without hyperon cores match $L_{\gamma}$
of young magnetars (with poloidal-dipolar field $B_{\textrm{dip}} \gtrsim
10^{14}$ G at the polar surface and $L_{\gamma} \gtrsim 10^{34}$ erg s$^{-1}$
at $t \lesssim 10^5$ yr) as well as mature, moderately magnetized stars (with
$B_{\textrm{dip}} \lesssim 10^{14}$ G and $10^{31} \ \textrm{erg s}^{-1}
\lesssim L_{\gamma} \lesssim 10^{32}$ erg s$^{-1}$ at $t \gtrsim 10^5$ yr). In
magnetars, the crustal temperature is almost independent of hyperon direct Urca
cooling in the core, regardless of whether the latter is suppressed or not by
hyperon superfluidity. The thermal luminosities of light magnetars without
hyperons and heavy magnetars with hyperons have $L_{\gamma}$ in the same range
and are almost indistinguishable. Likewise, $L_{\gamma}$ data of neutron stars
with $B_{\textrm{dip}} \lesssim 10^{14}$ G but with strong internal fields are
not suitable to extract information about the equation of state as long as
hyperons are superfluid, with maximum amplitude of the energy gaps of the order
$\approx 1$ MeV.
