From the website of Graedon:

Q. I must be especially tasty to mosquitoes, because they attack me and leave other folks alone. I have read in your column about hot water to stop itching. I’ve got a different solution: Warm a spoon in hot water and then put the back of the spoon on the bite. That stops the itch for several hours.

A. We have seen this suggestion on the Internet. It often includes the explanation that the heat denatures the protein that causes itching when mosquitoes inject it under the skin.

We suspect that the actual mechanism has more to do with the temporary effect of heat on nerve endings. Years ago, we read about using heat (in the form of hot tap water) to relieve itching in “Dermatology: Diagnosis and Treatment” (1961). The itch sensation can be overwhelmed for several hours with this approach.

Take care not to cause a burn, which would be worse than the mosquito bite.