Consider this as a possibility. A small self-propelled probe is created, its approximately the size of a football, and is very strong, made of materials with a melting point of a few thousand K. If this was dropped into one of the planet's various volcanic lava lakes, how far down could it travel? Or does the viscosity of the molten rock increase with a depth limiting it to a few 100m only?
This question could be answered on Worldbuilding SE, I'm just going to answer the part where the user asks how far it could travel and the materials that could possibly survive the probing mission.
First off I will start with listing Materials with high-melting points.
Tantalum Hafnium Carbide Alloy (3990℃)
Tantalum hafnium carbide alloy takes the 1st place in our list of the materials with the highest melting point.
Tantalum hafnium carbide alloy (Ta4HfC5) actually refers to tantalum and hafnium pentacarbonate compound, which has the highest melting point among known compounds. It can be considered to be composed of two binary compounds, tantalum carbide (melting point 3983 ℃) and hafnium carbide (melting point 3928℃).
Tantalum hafnium carbide alloys are used as heat resistant and high strength materials for rocket and jet engines, as well as parts for control and adjustment equipment.
Source. The article listed that tantalum Hafnium carbon alloy, "used as heat resistant and high strength materials for rocket and jet engines, as well as parts for control and adjustment equipment." So you could incorporate this material into you're probe
2. Graphite (3652 ℃)
Graphite ranks 2nd in our list of the materials with the highest melting point in the world.
Graphite is an allotrope of carbon, where three other carbon atoms (arranged in a honeycomb of hexagons) are covalently linked to each other to form covalent molecules. Due to its special structure, it has high-temperature resistance, electrical and thermal conductivity, lubricity, chemical stability, plasticity and so on.
Traditional graphite can be used as a refractory material, the conductive material, wear-resistant, and lubricating material casting, sand, die and high-temperature metallurgy material, while new graphite used as flexible graphite sealing material, car battery, new composite material, etc.
Graphite has a high melting point and can be used for many purposes, I recommend incorporating this into your probe.
3. Diamond (3550 ℃)
Diamond is another material that has very high melting points. Diamond is atomic crystal, while graphite is mixed crystal. The melting point of graphite crystal is higher than that of the diamond, which seems incredible.
However, the bond length of covalent bonds in the flake layer of graphite crystal is 1.42×10-10m, and the bond length of covalent bonds in the diamond crystal is 1.55×10-10m. Covalent bonds, the smaller the bond, the bigger the bond energy, the stronger the bond, the harder it is to break, the more energy you have to provide, so the melting point should be higher.
Diamond is used for cutting tools in arts and crafts and industry, such as drawing die, turning tool, thread cutter, durometer head, geological and petroleum drill bit, grinding wheel cutter, glass cutter, diamond pen, dresser knife, and abrasive material.
Although Diamonds have high melting points, they have limited purposes. I recommend using this to build your probe or using it as a shield for your probe.
I listed the top three in the article list. If you want to see more of the top ten check out this link: https://www.refractorymetal.org/list-of-metals-that-can-withstand-high-temperatures/
How to put your probe in the earth
Say, you have at least the top 3 or top 2 materials with the high melting points, you use expensive and futuristic technology and you have much research funding, but there is 1 thing in our way: How to put the probe into the earth.
The text you are about to read is based almost entirely on my observations
If your probe is the size of the football (Like you noted in your question), then I recommend digging a huge hole in a dormant or not-to-active volcanic geography after you do this (Do it extremely close to a dormant volcano, wearing a volcano suit), get a huge and long metal bar. hit the bar on the bottom of the hole. If you find extremely hot rock or magma/lava try a few more hits to molten or weak it further.
Once it's at the point of smoke or steam going out of the hole you made, I suggest using a non-electrical powered long shovel to dig further to make sure there is a lava flow "pipe" running in the crust, either carefully push ur probe under the lava once the lava is sinking back into the hole or simply throw your probe in a dormant volcano.
It's best the probe is scripted and computed to stay in the upper-middle mantle (For Data and safe exploration for your probe)