If you don't go too deep (a few thousand KM), the temperature is under 1000 degrees. We have plenty of materials than can handle that. For insulation use vacuum, or aerogel (which melts at 1,473 K) and is a phenomenal insulator. Add a large cold reservoir (liquid nitrogen) and you don't need a conventional A/C - it only has to last 42 minutes, and weight is not a problem.
The pressure is a much bigger problem. You can't bore a tunnel in the conventional sense since the rock is a liquid. You'd need some sort of wall, but I don't know if we have anything strong (and stable) enough. Most metals will oxidize and destroy themself at those temperatures.
Maybe a ceramic, or alumina coated metal. Perhaps a tungsten compound of some sort that is stable in oxygen at high temperature.
Another problem is the speed (reaching 1000 MPH), you'd need magnetic bearings (mag-lev), but magnets don't like being hot. The curie point of iron is 768 C, which is too low. Cobalt might work - but barely.