What exactly is convection? This is the process wherein heat transfer will occur. The less dense material will rise while those that are dense will start to sink. This is what happens with the thermometer, the mercury that is less dense will start to rise and in the process will show the temperature of the person.
There are also other examples of convection such as water boiling. It may start as room temperature but it would slowly boil. When ice melts, this is also another example of convection. A hot air balloon is another example because hot air is needed in order to make the hot air balloon rise up.
When heat is applied to a thermometer, the fluid inside will expand, not contract (fluid rises and occupies more volume). Also, it is possible for all three modes of transfer to apply to this example. convection and conduction definitely play a role; the effects of radiation may be negligible.convection- thermometer is exposed to ambient air or other fluid, conduction- heat flows through the glass to contact the liquid.