We report a finding of fast(exceeding 2,000 K/s) heating of polydimethylsiloxane(PDMS), one of the most commonly-used microchannel materials, under cyclic loadings at high(~MHz) frequencies. A microheater was created based on the finding. The heating mechanism utilized vibration damping of sound waves, which were generated and precisely manipulated using a conventional surface acoustic wave(SAW) microfluidic system, in PDMS. The penetration depths were measured to range from $210{\mu}m$ to $1290{\mu}m$, enough to cover most microchannel heights in microfluidic systems. The energy conversion efficiency was SAW frequency-dependent and measured to be the highest at around 30 MHz. Independent actuation of each interdigital transducer(IDT) enabled independent manipulation of SAWs, permitting spatiotemporal control of temperature on the microchip. All the advantages of this microheater facilitated a two-step continuous flow polymerase chain reaction(CFPCR) to achieve the billion-fold amplification of a 134 bp DNA amplicon in less than 3 min. In addition, a technique was developed for establishing dynamic free-form temperature gradients(TGs) in PDMS as well as in gases in contact with the PDMS.