We consider a thermodynamic machine in which the working fluid is a quantized harmonic oscillator that is controlled on timescales that are much faster than the oscillator period. We find that operation in this 'fast' regime allows access to a range of quantum thermodynamical behaviors that are otherwise inaccessible, including heat engine and refrigeration modes of operation, quantum squeezing, and transient cooling to temperatures below that of the cold bath. The machine involves rapid periodic squeezing operations and could potentially be constructed using pulsed optomechanical interactions. The prediction of rich behavior in the fast regime opens up new possibilities for quantum optomechanical machines and quantum thermodynamics.