What's the highest possible temperature that you can achieve?

There is no highest possible temperature that you can achieve. On a microscopic scale temperature is approximately the amount of energy each atom has. You can have a lowest possible temperature because you can have no energy at all. But you can give as much energy as you like to a particle but it will still just keep getting hotter and hotter. There's no theoretical maximum. There's maximum speed that things can reach, and that's the speed of light. But there's no maximum energy that they can have because at the speed of light, things have an infinite amount of energy.