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The 500 central pc of the Galaxy (hereafter GC) exhibit a widespread gas component with a kinetic temperature of 100-200 K. The bulk of this gas is not associated to the well-known thermal radio continuum or far infrared sources like Sgr A or Sgr B. How this gas is heated has been a longstanding problem. With the aim of studying the thermal balance of the neutral gas and dust in the GC, we have observed 18 molecular clouds located at projected distances far from thermal continuum sources with the Infrared Space Observatory (ISO). In this paper we present observations of several fine structure lines and the full continuum spectra of the dust between 40 and 190 microns. A warm dust component with a temperature between 27 and 42 K is needed to fit the spectra. We have compared the gas and the dust emission with the predictions from J-type and C-type shocks and photodissociation region (PDRs) models. We conclude that the dust and the fine structure lines observations are best explained by a PDR with a density of 10$^3$ cm^-3 and an incident far-ultraviolet field 10$^3$ times higher than the local interstellar radiation field. PDRs can naturally explain the discrepancy between the gas and the dust temperatures. However, these PDRs can only account for 10-30% of the total H2 column density with a temperature of ~ 150 K. We discuss other possible heating mechanisms (short version).