In this paper, we report a micromagnetic modeling study on the recording processes in heat-assisted magnetic recording. By solving coupled Landau-Lifshitz-Bloch equations, recording simulations are performed for granular FePt-L10 thin film media. The calculated signal-to-noise ratio shows strong dependence on recording field amplitude, especially for media of small size grains. It is found that low field amplitude yields unsaturated recording whereas high field amplitude causes transitions to be broadened immediately after writing. High thermal gradient will alleviate the transition broadening, allowing high field amplitude to be employed so that completed magnetization in the recorded bits can be achieved in small grin size media. The study concludes that the ability in obtaining the expected signal-to-noise ratio performance at very small grain pitches would critically rely on whether sufficiently high thermal gradient can be achieved in the media.