Yes, that seems to be normal.
Heat is generated whenever current passes through a material that has a non-zero resistance value (in Ohms). Such materials can be found (in abundance) in any electrical device, such as your phone - in the battery, the board, the processor, the antenna, etc. This means that heating will be experienced whenever an electrical device is used. The heating will be more pronounced when 1) the amount of current that is made to pass through the conducting materials is increased and 2) the passage of current is extended over a prolonged period of time.
For mobile phones, majority of the heating comes from the battery and the remainder come from the internal circuitry. The more power is used in a shorter period of time, the more heat will be generated. Activities that require more power include mobile data intensive activities, keeping the screen active (esp. at high brightness levels), constant and high processor activity, GSM antenna-related activities.
This means that browsing the net (which uses data and keeps the screen on), playing games (screen on, processor activity) and having poor signal (which even if you didn't mention may be worth looking at) will cause the increase in temperature (and the decrease in battery life) of your device.