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 ([OI] 63 and 146 micron , [CII] 158 micron , [SiII] 35 micron , [SI] 25 micron, and [FeII] 26 micron ), which are the main coolants of the gas with kinetic temperatures of several hundred K. We also present the full continuum spectra of the dust between 40 and 190 micron . All the clouds exhibit a cold dust component with a temperature of 15 K. A warmer dust component is also required to fit the spectra. The temperature of this dust component changes between 27 and 42 K from source to source. 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 103 cm-3 and an incident far-ultraviolet field 103 times higher than the local interstellar radiation field. The fine structure line emission arises in PDRs in the interface between a diffuse ionized gas component and the dense molecular clouds. The [CII] 158 micron and [SiII] 35 micron lines also have an important contribution from the ionized gas component. 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 for the rest the warm molecular gas, such as non-stationary PDRs, X-ray Dominated Regions (XDRs) or the dissipation of supersonic turbulence.