i will pay up to 500$
That's a lot of money for a relatively simple project. After having paid that money, you will have learned absolutely nothing, except how to pay for something you could (learn to) do yourself.
Even having paid for the development of the software, and integration of the hardware, there is no guarantee that the hardware delivered would plug and play in your environment.
Your internet service provider and relationship will have a lot to do with being able to access the Arduino/Ethernet shield from anywhere in the world.
Buying the shield yourself, and trying to run the examples provided would tell you whether or not the ability to remotely control the Arduino is even possible, given your internet access/service provider rules. If not, you are not out $500 plus the hardware.
If it is, adding a temperature sensor is easy. Making the Arduino/Ethernet shield serve up the correct page on demand is easy. If you run into difficulties, there are plenty of people here who will help you out for free.