Will I be able send a HTTP request using the Arduino Yún?
Looking at your other two questions as well I see you have had limited success with a ESP8266.  I have never used a Yun, but I haven't seen much good stuff about them on here.  If you want a Linux based none real time system then you may as well get a PI.

Most people seem to think the way to use an ESP8266 is to hook it up to an Arduino and use it as a 'serial over wifi' link.  You can do that, but its like owning a Porsche and Kia and always using the Kia on Motorway journeys.  The ESP8266 is an 80MHz chip with 0.5 MByte of RAM, and you could program it in just the same way as an Arduino if you download the board support package.  It does have only 10 Digital pins and 1 Analog (which I think has lower resolution that the Arduino), but that's where the Arduino comes in.  If you need to hook up lots of pins, then stick the Arduino on the I2C bus as a slave to the ESP.

Now I suspect you have an ESP-01 board and are wondering what the [heck] I am talking about, 10 pins.  The number '01' is the number of GPIO pins that are taken to the edge of the board, so really you want to look at ESP-12E or ESP-13E boards (they still cost about the same $1).  You might want to look at a Wemos D1 or a Node MCU.  Both are fully fledge dev boards, jus plug in the USB and away you go.

So to answer your question:

Get a Wemos D1, hook the hardware up like you wood the Arduino (thermistor and GPS - via SoftwareSerial) and then either code a web server to run on the Wemos or Get it to Post message to you favourite server (see examples for details of either approach)