Context. Measurements of intracluster gas temperatures out to large radii, where much of the galaxy cluster mass resides, are important for using clusters for precision cosmology and for studies of cluster physics. Previous attempts to measure robust temperatures at cluster virial radii have failed. Aims. The goal of this work is to measure the temperature profile of the very relaxed symmetric galaxy cluster Abell 2204 out to large radii, possibly reaching the virial radius. Methods. Taking advantage of its low particle background due to its low-Earth orbit, Suzaku data are used to measure the outer temperature profile of Abell 2204. These data are combined with Chandra and XMM-Newton data of the same cluster to make the connection to the inner regions, unresolved by Suzaku, and to determine the smearing due to Suzaku's point spread function. Results. The temperature profile of Abell 2204 is determined from ∼10 kpc to ∼1800 kpc, close to an estimate of r 200 (the approximation to the virial radius). The temperature rises steeply from below 4 keV in the very center up to more than 8 keV in the intermediate range and then decreases again to about 4 keV at the largest radii. Varying the measured particle background normalization artificially by ±10% does not change the results significantly. Several additional systematic effects are quantified, e.g., those due to the point spread function and astrophysical fore-and backgrounds. Predictions for outer temperature profiles based on hydrodynamic simulations show good agreement. In particular, we find the observed temperature profile to be slightly steeper but consistent with a drop of a factor of 0.6 from 0.3 r 200 to r 200 , as predicted by simulations. Conclusions. Intracluster gas temperature measurements up to r 200 seem feasible with Suzaku, after a careful analysis of the different background components and the effects of the point spread function. Such measurements now need to be performed for a statistical sample of clusters. The result obtained here indicates that numerical simulations capture the intracluster gas physics well in cluster outskirts.