Can I remotely access my router to check temps and webcam?

Well, if you have a weather station or camera it is possible on many routers to set up a "DMZ" item or two... Or port forwarding by another name.

You could, for example. forward all calls to port 80 to the camera (Streaming video)

There is a downside of this.

It is doubtful any hacker can hack a read only device like a camera.

Likewise the temp sensor. Though I know not the port.

But the problem is.. port 80 also is used by streaming video TO your computer. so you might need to "Un-forward" when at home.