My 2 cents: besides other possibilities some already mentioned in this trend, gien that it was bougt already used also could be tat what happened was that where it was working originally they had installed a female receptacle o the kind used by the male plug for 50A and preferred to change the male plug; or, maybe they were not using a dedicated circuit and the fuse would blow or the breaker open and they decided to change fuse and breaker from 30 to 50 and ten the plug too. There are a good number of possible speculations about the matter, but the practical point would be, is what I would do, to connect the drier, with an adapter or changing the plug for one of 30A, without working load for a work cycle and see how goes breaker or fuse, if no problem then turn it on again now with full working load and wait and see. If still no worries, all good and no need to change anything more than the plug; if with or without working load the fuse and or breaker open, then the machine needs a careful check up in inner circuits connections, motor, wiring, looking for shortcuts or burned up electric elements, or mechanical problems, that could be overloading the motor. As ppumkin said, a device marked on 30A of maximal input should not at all run over that, so to re-wire in 8 gauge and upgrade the value of circuit opener elements would just be inviting catastrophe if there's some problem underlying, or if there isn't any would be an idle and useless expense of money, work and time.
NEC 2008 430.22 Single Motor. (A) General. Conductors that supply a single motor used in a continuous duty application shall have an ampacity of not less than 125 percent of the motor’s full-load current rating as determined by 430.6(A)(1).30A * 125% = 37.5A. 80% of 30A breaker is 24A, 80% of a 40A breaker is 32A, 80% of 50A breaker is 40A. – Tester101♦ Jun 15 '12 at 12:22