The short answer is yes, the half life of a hot substance will be longer! But only very slightly. Though it's not because they're accelerating, but rather because they're moving faster.
Let's work out roughly how large the effect is. To make it as large as possible, let's take some very light particles so they move as fast as possible for a given kinetic energy. The lightest radioactive nucleus found in nature is tritium, an isotope of hydrogen consisting of a proton and two neutrons.
Molecules in a gas of tritium will have speeds roughly following the Maxwell-Boltzmann distribution, which we could use if we wanted to be really precise, but to get a ballpark figure we can estimate the speed of the molecules using just dimensional analysis. The only scales in the problem are the mass of the molecules $m$, and the temperature $T$, and we'll also need Boltzmann's constant to convert from units of temperature to energy. The only speed we can build from this is
$$
v \sim \sqrt{\frac{kT}{m}}
$$
Putting in the mass of a tritium molecule (6 nucleon masses, because there are two atoms in each gas molecule), and room temperature, we get around 600 metres per second, or 2 millionths of the speed of light.
The time-dilation effect will change the half-life by a factor of $\gamma$, which is
$$
\gamma = \frac{1}{\sqrt{1-v^2/c^2}} \approx 1+\frac{v^2}{2c^2}
$$
where the approximation uses the binomial theorem, and works for speeds much less then $c$. For our room-temperature tritium, this is roughly an extra factor of $2*10^{-12}$: a really tiny amount! The tritium half-life is 12 years, and the relativistic effect of room temperature adds about a millisecond to that. Needless to say, this would be a very hard effect to measure!
