I am sorry that your class has waited so long for the answer to your question. This topic probably falls outside the expertise of all the Solar Week scientists. Like most scientists, we specialize in one particular research area. During Solar Week, students ask many questions that fall outside our expertise, such as questions about earthquakes, life on other planets, and astronauts. Sometimes one of us might know an answer to a question even though it falls outside our research area, since we have heard people discussing this topic at conferences or have read about it in our spare time. However, most of the time we would have to look up the answer to these questions in a book or on the Internet.
I can't give you an exact answer to your question, but after searching the Internet I can tell you a little about the orbits of a few spacecraft and make an educated guess which one has made the closest approach to the Sun. However, this is only a guess, and I don't know a definite answer.
I would guess that the spacecraft to make the closest approach to the Sun so far is probably the Mariner 10 mission. Mariner 10 was the first mission to use the gravitational attraction of one planet to reach another and the only mission so far to study the planet Mercury up close. During its two-year mission, Mariner 10 transmitted over 12,000 images of Mercury and Venus. The Mariner 10 mission ended in March 1975, but the spacecraft is still orbiting the sun. However, the electronic systems on board Mariner 10 have probably been destroyed by solar radiation. I couldn't find any information about what the actual perihelion (closest approach to the Sun) distance for Mariner 10 was on the Internet during my quick search. Maybe your class can try searching the Internet for this information.
The MESSENGER mission is currently on its way to the planet Mercury. I do not know whether or not MESSENGER will fly closer to the Sun than Mariner 10. On the MESSENGER web site (http://messenger.jhuapl.edu/), it says that MESSENGER's average distance to Sun when it reaches Mercury in 2011 will be 0.388 AU ~ 58,200,000 kilometers = 36,000,000 miles. In a few years, the European Space Agency is planning to launch the Bepi Colombo mission to Mercury (http://sci.esa.int/science-e/www/area/index.cfm?fareaid=30). I did not see anything during my quick Internet search that said how close to the Sun they plan to send the Bepi Colombo mission.
Many of the missions NASA has launched to study the Sun do not actually get that close to the Sun. For example, SOHO is about 150,703,456 kilometers (92 million miles) from the Sun and only about 1,528,483 Kilometers (1 million miles) from the Earth (three times farther than the moon). SOHO actually orbits around a mathematical point between the Earth and the Sun known as the Lagrange point or the L1 point. The closest approach to the Sun made by the Ulysses mission to study the Sun was 200 million kilometers (124 million miles) in 1995.
Kris