The CPU impacts the overall mobile gaming experience. Qualcomm's SoCs works best and are capable of handling almost all high end games. Mediatek will save you a lot of money and have recently came up with good mobile chipsets, but are not able to beat Snapdragon, Adreno, Apple A series in all benchmarks. Moreover, it's impossible to hold a phone with heating problems. A good processing unit would dissipate most of the heating issues. But remember, high end gaming would lead to some heating in almost all smartphones, even the latest phones. Minimum a dual-core processor with good speeds in both CPUs is recommended. Also, you need lots of free RAM. So opt for at least a 2GB RAM device. HD display would suffice, but yes, you can take your games to the next level will more added pixels, but that will drain your battery too soon. Battery too plays a very important role in a good gaming phone. A good backup is must and that too with quich charging.