Old-Fashioned Candy/Deep-Fry Thermometer - How Shallow Can I Go?
That is probably not deep enough to get an accurate reading. It varies with the thermometer, but usually you need at least a couple of centimetres to be submerged to get an accurate reading. Also, unless you are super careful, it will be nearly impossible to stop the thermometer touching the bottom of the pan. In my experience the clips on these doohickies are terrible for adjusting the angle of the thermometer.

When shallow frying in this manner I usually just go by rules of thumb. One that has never let me down is to use a wooden chopstick. When you think the oil is getting hot enough, place the tip of the chopstick in the oil. If bubbles rapidly appear around the chopstick, you're hot to trot.