  Specific heat C_{p}(T) measurements of the heavy fermion normal-spinel
structure compound LiV_{2}O_{4} were carried out using a heat-pulse calorimeter
over the temperature T range from 1.2 to 108 K. The electronic specific heat
C_{e}(T) of LiV_{2}O_{4} is extracted from the C_{p}(T) data using the lattice
contribution obtained for LiTi_{2}O_{4}, a superconductor with T_{c} = 11.8 K.
The electronic specific heat coefficient \gamma(T) = C_{e}(T)/T of LiV_{2}O_{4}
is found to be 0.42 and 0.43 J/mol K^2 at T = 1 K for two different high
magnetic purity samples, respectively. \gamma(T) decreases rapidly with
increasing temperature from 4 to 30 K and then decreases much more slowly from
0.13 J/mol K^2 at 30 K to 0.08 J/mol K^2 at 108 K. The C_{e}(T) is compared
with theoretical predictions for the spin S = 1/2 Kondo model, a generic Fermi
liquid model, and an antiferromagnetically coupled quantum-disordered metal.
Each of these theories can adequately describe C_{e}(T) in the Fermi liquid
regime at low (~ 1 to 10 K) temperatures, consistently yielding a large
extrapolated \gamma(0) = 428(3) mJ/mol K^2. However, none of these theories
describes C_{e}(T) from ~ 10 K to 108 K. Our C_{e}(T) data are also in severe
disagreement with the magnetic specific heat of the spin S = 1/2 Heisenberg
model. Thermal expansion measurements of LiV_{2}O_{4} were carried out from 4.4
to 297 K using a differential capacitance dilatometer. Strong increases in the
thermal expansion coefficient and Gr\"uneisen parameter \Gamma are found below
\~ 20 K, confirming the results of Chmaissem et al. [Phys. Rev. Lett. 79, 4866
(1997)] obtained using neutron diffraction. We estimate that \Gamma(0) is about
11.4.
