you have two parts to your problem. The first thing you need to think about is the details of each of these areas.
First, you have actual readings. Second, you want “control” of, I assume, your home air conditioning/heating system.
So for actual readings, I assume your data is already successfully shown on a web page? If not, that’s the first step - there are many “Web server” projects on codeshare that will get past this. But this will only be visible when you’re accessing it from within your home network. To make it accessible when you’re outside the home you can do one of two things. You could simply use your home router to “publish” the web server and make it accessible to the wider internet (yes there are security aspects you need to think about). Or, you could send your data to a public service that stores and displays your data, and you access that from the internet directly. (I have a Fez Panda pushing data to this site every 10 minutes http://pvoutput.org/intraday.jsp?sid=503 ).
Then you want control over the environment. You need to think about what kind of heating/cooling you have, you need to think about what access you can safely get to that system, and then you need to figure out how to send heating/cooling commands. Again, once you conquer that when you’re “inside” you can think about the outside aspects. Have you already tried this and achieved control ? Another part of this is to figure out how you securely provide access to the control button over the internet - again there are 3rd party systems that can avoid you needing to directly open your device to incoming requests from the internet but you then don’t control the access, someone else does (and that may be a bigger concern for you?)
So my general suggestion is figure out the components, then figure out how you connect the components you figured out earlier to achieve the outcomes you want.