Use a SIM card module (SIM808) with the less battery possible
Probably the best way is to completely switch of both the Arduino and GSM ... Let them start up by a timer chip (a simple 555 should suffice if using a fixed time anyway)... than let the Arduino start up, initialize the GSM and after the send, switch down. 

6 hours between every communication seems worthwhile to switch it off completely and take the startup of the Arduino and GSM as only advantage.