It is possible to send a probe deep within the Earth?
First, read these three very relevant questions and answers:
Why the &quot;Mission to Earth’s core&quot; proposal suggests using liquid iron instead of lead?
Can we really travel through earth&#39;s core?
Hypothetically, what would happen to the earth if a large hole was drilled through the center?


It is possible to send a probe deep within the Earth?

No.
Here's why:
First, there is a very common misconception that there's some sort of magma ocean underneath the crust. No - there isn't. The Earth's mantle is overwhelmingly solid rock. There are very small and localised places where you have melting, and that's where you have volcanoes (if it reaches the surface - most often it doesn't).
Second, even if you go to a volcano and drop your probe there, there is no simple tube that goes down. A volcano &quot;plumbing&quot; system is more like a maze with bifurcations, bends, kinks, and all of that. Not only that, you are going against the flow. You've probably seen videos of erupting lava flows (one, two). These things are massive and fast. Your probe will have to go against the flow in that thing. It will be worse than trying to go upstream in river rapids.
Third, even if you somehow manage to make a probe that autonomously navigates upstream in thin underground lava corridors with surprise bends, you have to remember the underground magma chambers are not 100% liquid. They are what we call &quot;crystal mushes&quot;, which is a pile of small crystals (i.e., bits of rock) with liquid in between. Think more like wet sand, than pure liquid. So you're not swimming in something with no resistance, you also actively have more solids out of your way.
Fourth, molten rocks are extremely corrosive. You were talking about materials with high melting points. That's not your problem. Even the hottest lavas only get to about 1400 °C. We have relatively cheap materials that will melt at much higher temperatures. The issue is the reaction between the magma and the materials into making new materials, or dissolving completely in the magma. As an illustration, consider sodium chloride. Salt. The point at which it melts, if you stick it into a furnace is around 800 °C. Surely, that's much above the temperature of let's say an ocean, and it might be a good idea to make submarines out of salt! Clearly, bad idea. Because the salt will just dissolve into the ocean. Whether it melts or not is irrelevant. So that's the big problem with your probes - the magma will simply dissolve it.

So to sum up, you need your probe to be able to navigate in the dark and propel itself upstream in magma, be able to dig and clear space up front so it can move forward, and made of a material which is inert to the magma. Sorry - not happening. But a fun thought experiment nonetheless.