An important advantage of tanning indoors is that the amount of UV light you receive is regulated, and there is greater control of exposure. You can gradually increase your exposure times to get a tan, while helping to minimize sunburn. Your eyelids do not provide adequate protection from UV light. Although there may be no immediate symptoms, damage may be occuring to your eyes which can lead to vision problems. Probably not for the reason you think, either.
Excess heat can be harmful to the pregnancy and can cause complications.
You should not tan while you are pregnant. They are a type of fungus, similar to dandiff, and are harmless. They can be pretty common to tanners and are easily treatable. There are sun spot products available in your salon which should eliminate the problem. If your salon doesn't carry any, then try a dandriff shampoo, such as Tegrin.