We present the results from the Suzaku satellite of the surrounding region of a galaxy cluster , A2744 , at z = 0.3 . To search for oxygen emission lines from the warm-hot intergalactic medium ( WHIM ) , we analyzed X-ray spectra from two northeast regions 2.2–3.3 and 3.3–4.4 Mpc from the center of the cluster , which offers the first test on the presence of a WHIM near the typical accretion shock radius ( \sim 2 r _ { 200 } ) predicted by hydrodynamical simulations . For the 2.2–3.3 Mpc region , the spectral fit significantly ( 99.2 % significance ) improved when we include O \emissiontype VII and O \emissiontype VIII lines in the spectral model . A comparable WHIM surface brightness was obtained in the 3.3–4.4 Mpc region and the redshift of O \emissiontype VIII line is consistent with z = 0.3 within errors . The present results support that the observed soft X-ray emission originated from the WHIM . However , considering both statistical and systematic uncertainties , O \emissiontype VIII detection in the northeast regions was marginal . The surface brightness of the O \emissiontype VIII line in { 10 ^ { -7 } photons cm ^ { -2 } s ^ { -1 } arcmin ^ { -2 } } was measured to be 2.7 \pm 1.0 , 2.1 \pm 1.2 for the 2.2–3.3 , 3.3–4.4 Mpc regions , giving the upper limit on the baryon overdensity of \delta = 319 ( < 443 ) , 283 ( < 446 ) , respectively . This is comparable with previous observations of cluster outskirts and their theoretical predictions . The future prospect for WHIM detection using the Athena X-IFU micro-calorimeter is briefly discussed here . In addition , we also derived the ICM temperature distribution of A2744 to detect a clear discontinuity at the location of the radio relic . This suggests that the cluster has undergone strong shock heating by mass accretion along the filament .