Storing wallet key for automatic transactions Is there any way to do this? For example I don't even want to know what my wallet is, only my server (intranet), so that it can make automatic transactions for me based on thresholds.

Or should I not be looking at this approach at all? How do the big exchanges do it? Can I automate transactions securely without needing to type a password every time?

The context here is a mining network
It depends on the type of wallet you are using in the server. 
you can write your own node to publish transactions (very hard)
you can use 3rd party services like blockchain info (easy)
you can use a wallet that has an api (like bitcoin-core has json rpc) 
then you write a program that call this wallet to generate tx
it uses the build in security of the wallet