The temperature lowers considerably. In the video, the initial temperature is 27.4 degrees Celsius, and this lowers to 7.6 degrees Celsius.
The enthalpy of solution of NH4NO3 is 25.7 kJ/mol. Heat is therefore absorbed from the surroundings as the salt dissolves in water. Naturally, this heat absorption lowers the temperature of the beaker and its surroundings, so the thermometer registers a lower temperature.
Commercial ice packs that utilize this reaction contain 4.4 moles of water for each mole of NH4NO3. When these packs are activated, the temperature of the ice pack drops to a minimum of -11 degrees Celsius.