Does cooking ginger reduce its anti-nausea effect?
Good news! Some Australians have published on the stability of aqueous gingerol at elevated temperatures: http://onlinelibrary.wiley.com/doi/10.1002/jps.1116/full

Gingerol turns out to be stable enough to make a cup of tea with at neutral pH. They also note that gingerol and its primary decomposition product form a 50-50 mixture that doesn't degrade further over shortish time periods, and that the decomposition product is probably restored to gingerol in the stomach's acidic pH -- so you're good to make your tea, and probably to hold on to it for at least a few days.