WebAPI to interact with bitcoin wallet
You actually have several options, but they all relate to what your hot wallet actually is, and how you want to interact with it.

For example, you could have bitcoind running on a different server, and allow it to accept RPC commands from your web server.  These commands could either be issued by calling the command line on your server, or by adding RPC support directly into your web application.

You could also skip using an "out of the box" wallet like bitcoind, and instead add wallet features directly into your web application using a library like NBitcoin (since it sounds like you are using .NET).  In this scenario, your web application would actually be your hot wallet, and you would only build out the wallet capabilities that you plan on using.

In either of these cases, however, I would advise you to keep wallet functionality off your public facing web server, and make sure that the server handling the actual signing of transactions and storage of private keys is only accessible from your web server (with proper authentication), and not the internet at large.  When bitcoin is involved, it's best to limit your attack surface.