Firstly, as the comments said, there is no solid surface on the sun. It's a big ball of plasma which undergoes fusion (process of atoms combining and releasing energy). Secondly, an object can't "float" on the sun. A possible but very unlikely theory would be to have a probe that floats because of convection. Constant heat acting on the bottom of it and colder areas coming down (similar to how birds use warm air to rise), however it needs to overcome the Sun's gravity and convection only occurs in the convection zone which makes it impossible. Another possibility is to create a probe that continuously fires its thrusters to stay afloat. But this is useless and uses a lot of fuel. Your best bet would be to make a probe that orbits the Sun, however that is also very hard to do for many reasons. First, you need to get to the Sun. Most probes go into the outer solar system (such as Jupiter) to use a gravity assist to slow down and orbit close to the sun, similar to the Ulysses spacecraft. This is the trajectory of the Ulysses Spacecraft (note how it uses Jupiter to slow down). Also, in order to orbit that close to the sun, you need tremendous orbital velocity. You can calculate how much orbital velocity is needed with the Vis-Viva equation.
These are just ways to get close to the Sun, another big problem is to use a material that can survive the intense heat, and electromagnetic radiation. However there is an advantage, heat is not the same as temperature. Heat is the amount of energy transferred while temperature measures how much the particles move. Here's an example, a cup of boiling water and a tub of boiling water are both 100 degrees Celsius, however the tub has more heat energy because it has more mass (molecules) even though they're both the same temperature. Same applies to space. Space is virtually a vacuum so there are very few particles thus your spacecraft can survive. This is how the Parker Solar Probe survives the heat of the Sun. As for thermal radiation, it's a method of heat transfer that doesn't require a medium and travels through waves in a straight line. A workaround through that is to have a reflective shield that reflects the radiation and prevents it from travelling to the other side of the shield similar to the previously mentioned Parker Solar Probe.