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Using 1D and 2D cooling codes we study thermal emission from neutron starswith steady state internal heaters of various intensities and geometries (blobsor spherical layers) located at different depths in the crust. The generatedheat tends to propagate radially, from the heater down to the stellar core andup to the surface; it is also emitted by neutrinos. In local regions near theheater the results are well described with the 1D code. The heater's regionprojects onto the stellar surface forming a hot spot. There are two heatpropagation regimes. In the first, conduction outflow regime (realized at heatrates $H_0 \lesssim 10^{20}$ erg cm$^{-3}$ s$^{-1}$ or temperatures$T_\mathrm{h} \lesssim 10^9$ K in the heater) the thermal surface emission ofthe star depends on the heater's power and neutrino emission in the stellarcore. In the second, neutrino outflow regime ($H_0 \gtrsim 10^{20}$ ergcm$^{-3}$ s$^{-1}$ or $T_\mathrm{h} \gtrsim 10^9$ K) the surface thermalemission becomes independent of heater's power and the physics of the core. Thelargest (a few per cent) fraction of heat power is carried to the surface ifthe heater is in the outer crust and the heat regime is intermediate. Theresults can be used for modeling young cooling neutron stars (prior to the endof internal thermal relaxation), neutron stars in X-ray transients, magnetarsand high-$B$ pulsars, as well as merging neutron stars.

Thermal emission of neutron stars with internal heaters