  A simple way to visualize event-by-event average $p_T$ fluctuations is by
assuming that each collision has a different temperature parameter (inverse
$p_T$ slope) and that the ensemble of events has a temperature distribution
about the mean, $<T>$, with standard deviation $\sigma_T$. PHENIX characterizes
the non-random fluctuation of $M_{p_T}$, the event-by-event average $p_T$, by
$F_{p_T}$, the fractional difference of the standard deviation of the data from
that of a random sample obtained with mixed events. This can be related to the
temperature fluctuation:
  \[ F_{p_T}=\sigma^{\rm data}_{M_{p_T}}/\sigma^{\rm
random}_{M_{p_T}}-1\simeq(< n > -1) \sigma^2_{T}/< T>^2 \]
  Combining this with the Gavai, {\it et al.},\cite{Gavai05} and Korus, {\it et
al.},\cite{Korus} definitions of the specific heat per particle, a simple
relationship is obtained:
  \[ c_v/T^3={\mean{n}\over \mean{N_{tot}}} {1\over F_{p_T}} \]
  $F_{p_T}$ is measured with a fraction $\mean{n}/\mean{N_{tot}}$ of the total
particles produced, a purely geometrical factor representing the fractional
acceptance, $\sim 1/33$ in PHENIX. Gavai, {\it et al.} predict that
$c_v/T^3=15$, which corresponds to $F_{p_T}\sim 0.20$% in PHENIX, which may be
accessible by measurements of $M_{p_T}$ in the range $0.2\leq p_T\leq 0.6$
GeV/c. In order to test the Gavai, {\it et al.} prediction that $c_v/T^3$ is
reduced in a QGP compared to the ideal gas value (15 compared to 21), precision
measurements of $F_{p_T}$ in the range 0.20% for $0.2\leq p_T\leq 0.6$ GeV/c
may be practical.
