What does spray tan solution do to a temporary tattoo?

Assuming you're talking about a stick on/transfer temporary tattoo, and not henna or other ink, spray on tans will likely cover up your temporary tattoos slightly. Depending on the oil and chemical content, they may also degrade the glue that holds the tattoo design on.

To be safe, if you want your temporary tattoo to last, cover it with a bandage when getting spray tan solution applied. Then rub the spray tan around then edges of the tattoo with your fingers.