There's a couple of things happening here.
Because fingers are at the extremities of a human body, the temperature there is a bit lower compared to the core body temperature.
While a healthy individual has a core body temperature of approximately 37°C, mean skin temperature can be as low as 32-35°C.
Another thing that is happening is that while you may be holding a thermometer such as a thermocouple within your fingers (say, index finger and thumb), it is possible that you are not actually covering it completely. As a result, the sensor will be reading a lower temperature to what you expect.
Another thing to remember about the thermocouple is that in terms of its speed, it is not very fast because of the amount of mass it contains. As a result, it take time for this mass to adjust when the temperature around it changes, so you have to allow enough time for your readings to settle.