Internal energy is linked to the temperature of matter but the two are very different things:
Heating water causes the water molecules to gain kinetic energy and speed up. It takes more energy to raise the temperature of a large amount of water because more molecules need to have their speed changed.
In the diagrams above the two beakers have been heated by the same Bunsen burner for the same amount of time, so both have been given the same amount of energy. However, the smaller beaker has had a bigger temperature rise because the same energy has been given to a smaller number of particles so each particle is moving faster than those in the other beaker.
Imagine a teaspoon of boiling water at 100 degrees Celsius (°C) and a large bowl of water at room temperature: