The CC3000 chip from Texas Instruments is an amazing module for embedded application. When it first came out, every body got very excited. However, over the year, it appears to be an difficult module to work with. After lots of firmware update, now it appears to be more workable than before.
In this project, I am using CC3000 (firmware v1.32 - Patch 1.14 why TI??) with Arduino Uno. I used Arafruit host library and ThingSpeak service for online interfacing. The similar application was developed by M.Schwartz and was posted in Adafruit learning center. In that tutorial, he used Xively service for online interfacing. To me it seems that he was annoyed by the bugs in CC3000 and put watch dog timer in every steps to recover from the notorious CC3000 freezing issue. I also faced the same problem before. After the latest patch update, it seems that the CC3000 performance has been improved significantly.
The circuit connections for WiFi and DHT11 temperature sensor remain same as Schwartz's design as shown here. For ThingSpeak account, please visit their website and open a free account. Log in to your account and open a new channel. In channel setting, most important part is, Field boxes. Check mark on the "add field" box to activate more channels. In my tutorial, I used only 2 channels and changed them as Temperature and Humidity. Next, the most important part is API Keys. Copy the "Write API Key" to write a data to the web server. Replace the "your api key"; in the code with your API key. Here is the Arduino sketch,
Here is my sensor reading in ThingSpeak website.