We have examined the use of CH3C2H as temperature probe in dense cloud cores and find that the J = 6 --> 5 (K = 0, 1, 2) transitions are a good probe of the gas kinetic temperature. We have applied these results by observing the CH3C2H J = 6 --> 5 transition in dense cores in Orion, M17, and Cepheus A. These observations were supplemented by observations of another commonly used temperature tracer-the J = 1 --> 0 transition of (CO)-C-12. A comparison or temperatures obtained from the two thermometers in Orion and M17 show significant differences, with temperatures inferred from CO in general significantly greater than those inferred from CH3C2H. We propose that the differences result from actual differences in the emission region along the line of sight with CO tracing the low-density foreground gas and CH3C2H the cooler high-density gas. The lack of agreement between the results from the low-density thermometer, CO, and those from the high-density thermometer, CH3C2H, also suggests that different heating mechanisms are required for the two density regimes.