A hot work tool steel family with exceptional thermal diffusivity, toughness (both fracture toughness and notch sensitivity resilience CVN—charpy V-notch) and trough hardenability has been developed. Mechanical resistance and yield strength at room and high temperatures (above 600° C.) are also high, because the tool steels of the present invention present a high alloying level despite the high thermal conductivity. Given the exceptional resistance to thermal fatigue and thermal shock, wear resistance can be severely increased for many applications requiring simultaneously resistance to thermal cracking and wear like is the case for some forging and some parts of die casting dies.