Original post by Noble.The height an aircraft cruises at is primarily determined by the weight of the aircraft. Which is why, on a long-haul flight, you may initially climb to FL280 (28,000ft above sea level) but by the end of the flight you're at FL380 (38,000ft ASL) when the aircraft is potentially up to 130 tonnes lighter after burning fuel; there is essentially an optimum altitude to fly at taking into consideration the fact that you burn less fuel at higher altitudes, for a fixed thrust setting, but you also need more thrust to maintain a certain altitude the higher you climb (so there's a trade-off). The reason aircraft don't just go straight to the final cruising altitude is, in part, an obvious one (weight - there isn't enough thrust to get there) but there is also a secondary aerodynamic reason - for a fixed gross weight, climbing higher decreases the gap between the stall speed and the critical mach number, both of which causes an aircraft to stall if the airspeed reaches either. In an extreme example, on a long-haul (10+ hour) flight (in say a 777 or a 747) taking off at the maximum take-off weight the flight management computer will probably recommend an initial cruising altitude of FL280-FL300, but in reality the aircraft could probably make it to FL340-FL360, but the reason you wouldn't climb to that altitude is the secondary reason mentioned above - the aircraft would be operating on such tight margins (between the stall speed and critical mach number) that any big fluctuation in wind speed, or hitting any turbulence, could result in a stall (if you're interested in this more, look up Q-corner/Coffin corner on Wikipedia).
The fact they were cruising at FL320 and not FL340 is probably because the optimum cruising level was less than FL340. So climbing up to FL380 would put the aircraft in a significantly more vulnerable position in the event they hit turbulence. However, this would be such an odd thing for a pilot to do, especially a pilot that regularly flies in that area because generally CBs exist up to FL500 in the tropics - i.e. you can't climb out of it - so there may have been other factors in requesting this climb (but still, it's a foolish thing to do). There is also the fact that at a higher altitude, with a higher thrust setting, they would have had much less "power on tap", so in the event the aircraft got close to the stall speed and alpha protection kicked in, the engines switching to maximum thrust would've had little effect on increasing the airspeed - whereas at a lower altitude, maintaining the same height, with a lower thrust setting, the engines essentially are in a much better position at maintaining airspeed (and with a greater margin for error as well). In many respects, if you're caught in a situation where you can't fly around weather, you're better off flying straight into it at an altitude the aircraft is 'happy' to fly at with a slight reduction in speed, than you would be trying to climb out of it.