Yes, it is possible that a metal probe would cause an electrolytic reaction. Use it by all means, but put it into the solution, take the temperature measurement and then remove it. Doing this will avoid any problem and the time in the solution is then insignificant.
To "measure" temperature without a thermometer, just heat the water to a simmer (you see bubbles form on the bottom of the reaction vessel, but the bubbles disappear before they reach the surface of the water).