All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The central bank has many functions, including what is permissible and what is forbidden. It is not like the Riba-based commercial banks, whose activities are primarily based on Riba.
The existence of Central Banks is essential as they are the ones who issue money and keep (save) the country's reserves of gold, foreign currencies and other necessary services.
Therefore, providing any lawful service, such as designing air conditioning system and other things in which a person does not engage in something forbidden, or directly help in it, is permissible.
Allah knows best.