This was the info about underarm from kidspot

"Taking an underarm temperature
Taking a temperature under the arm is called an axillary temperature. Taking a temperature under the arm gives the least accurate reading. Under arm temperatures can be up to 0.5° to 1.2°C lower than actual body temperature. However, taking your child's temperature under the arm is usually easier and faster than struggling to get an oral temperature from a wriggling and/or crying child."

So there are pros and cons to all methods.