Yes you can use the pro mini to do these things.
I would recommend you buy an Arduino UNO though, do your development on it then use your mini for the final product.
Start with the basic sketches to learn programming.
Google, LCD Arduino, for examples.
Google, temperature Arduino, for examples.
See:
http://pulsesensor.com/2011/08/01/anatomy-of-the-diy-heart-rate-monitor/