Martens hardness

Martens hardness isn't a common term – you probably mean the hardness of martensite, which forms when steel cools quickly. If you cool too fast during welding, hard, brittle martensite forms, which tends to crack. Hardness testing after cooling shows you whether the structure is too hard and thus prone to cracking. In practice, this means: let such steels cool slowly or stress-relieve after welding, otherwise you'll get cold cracks. You don't measure hardness during cooling, but only on the finished workpiece.