By adapters do you mean on the mechanical side, or on the electronics side? If the entire drivetrain has been designed for 24V, you're obviously risking damage by going to 36. Do you know if the controller can take such voltages?
This battery doesn't look very powerful either, and you need to check its current/power ratings. Just because a battery runs on 36V doesn't mean it can necessarily give out more power than a 24V one.