How can you speed up a genoise cake mixing?
I suspect that the purpose of the double boiler is to bring the eggs up to room temperature, which isn't going to make that much of a difference. Most recipes would say that the process will take 10 minutes, but you may be able to speed things up marginally:


Use a bowl that concentrates the eggs in as small an area as possible so your beater blades contact as much eggs as possible per rotation. A narrow, tall bowl is better than a wide, shallow one. If you don't have that then tip the bowl you do have so it all concentrates in one area
Use fresh eggs, I've found that fresher eggs take air better. It's true for egg whites at least, so I suspect it will be for whole eggs as well
Let the eggs come up to room temperature before using them, that way you don't need the double boiler setup, which will give you more flexibility when it comes to bowls. If you don't have 20-30 minutes to let the eggs warm naturally then 5 minutes submerged in tepid water will do the same thing 


Other than that the only thing I can recommend is to buy a stand mixer or cultivate patience. Preferably both.