As part of the Herschel Guaranteed Time Key Project MESS (Mass loss of Evolved StarS) we have imaged a sample of planetary nebulae. In this paper we present the PACS and SPIRE images of the classical bipolar planetary nebula NGC 650. We used these images to derive a temperature map of the dust. We also constructed a photoionization and dust radiative transfer model using the spectral synthesis code Cloudy. To constrain this model, we used the PACS and SPIRE fluxes and combined these with hitherto unpublished IUE and Spitzer IRS spectra as well as various other data from the literature. The temperature map combined with the photoionization model were used to study various aspects of the central star, the nebula, and in particular the dust grains in the nebula. The central star parameters are determined to be T_eff = 208 kK and L = 261 L_sol assuming a distance of 1200 pc. The stellar temperature is much higher than previously published values. We confirm that the nebula is carbon-rich with a C/O ratio of 2.1. The nebular abundances are typical for a type IIa planetary nebula. With the photoionization model we determined that the grains in the ionized nebula are large (assuming single-sized grains, they would have a radius of 0.15 micron. Most likely these large grains were inherited from the asymptotic giant branch phase. The PACS 70/160 micron temperature map shows evidence for two radiation components heating the grains. The first component is direct emission from the central star, while the second component is diffuse emission from the ionized gas (mainly Ly alpha). We show that previous suggestions that there is a photo-dissociation region surrounding the ionized region are incorrect. The neutral material resides in dense clumps inside the ionized region. These may also harbor stochastically heated very small grains in addition to the large grains.
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