When matter is heated to very high temperatures, it turns into a plasma. Such plasma can emit X-rays.
Discharge plasma sources
X-rays are emitted from hot plasmas. When the current in an electric discharge in a low pressure gas, e.g. nitrogen, is increasing extremely fast by discharging a huge capacitor, the resulting strong magnetic field is pinching the discharge to an increasingly small volume with rising temperature until the discharge is converted to a plasma.
Laser induced plasma sources
When the light of a high energy laser pulse hits a target, heating it to plasma temperatures, X-rays are emitted.