What you ask is actually not a physics question. It's an engineering question. There's really not all that much of a difference physics wise between a ball of protons and a marble.
Of course, from an engineering perspective, they are monumentally different.
Consider this line of reasoning. The LHC hit 5.5 trillion degrees C a few years back. It used roughly 10^-16kg worth of protons to do so (ignoring relativistic effects). A grain of sand is roughly 10^-5kg, so we will need to scale up the LHC by 10^11. We'll start by assuming that scaling is linear. It might not actually be linear when reality gets in the way.
The LHC uses about 120MW of power. Its biggest limitation is that it quenches the superconducting magnets a few times a day, and has to start over We'll say 4 times. That's 6 hours to do an experiment to generate the highest heats possible. 6 hours at 120MW is about 2.5TJ of energy. So we used 2.5TJ of energy to heat up that little tiny mass to 5.5 trillion degrees.
if we scale that, 2.5TJ * 10^11 is about 10^23 J of energy. From one of my favorite Wikipedia pages, Orders of Magnitude (Energy), that's roughly 10 times the available fossil fuels.
Since you explicitly forbid nuclear power, and described your intent of avoiding including stars, we're going to have to work with what we have. Fossil fuels it is.
So that should be enough to show that this is really an engineering problem, not a physics problem. Very roughly, you should be able to get an object the size of a grain of sand up to about 500 billion degrees using similar techniques to the LHC, assuming they scale linearly. In practice, I'm sure we'll find the LHC doesn't scale this way. But also in practice, I'm assuming you wont be permitted to consume the planet's entire fossil fuel reserves in the effort to make something really hot.
So it's not a physics question, and maybe it's not even an engineering question. Maybe its a politics question!