  A detailed description of an isoperibol calorimeter for temperatures between
0.05 and 4 K is presented. The proposed setup can provide absolute values of
the heat capacity $C$ of small samples (typically 1 mg). The extremely simple
design of the sample platform, based on a sapphire substrate, and the
experimental setup, which makes use only of a lock-in amplifier and a
temperature controller, make the construction of such a calorimeter easy and
inexpensive. The thermal-relaxation method is employed, which utilizes a
permanent thermal link $k$ between the sample platform and the low-temperature
bath. The temperature dependence of $k(T)$ is shown for several platforms
throughout the entire temperature range: $k(T)/T$ is nearly constant down to 1
K, where it starts to decrease smoothly. The observed behavior is thoroughly
explained by considering the thermal resistances of the platform constituents.
A comparison between the values of $k(T)/T$ for platforms based on sapphire and
on silver is presented where no significant difference has been observed. Each
platform can be assembled to have a particular value of $k/T$ at 1 K. Since the
sample relaxation time $\tau \sim C/k$, $k(T)$ can be adjusted to $C(T)$ to
give a reasonably fast measuring time: Here, it is demonstrated how this
calorimeter can be used in so-called single-shot refrigerators ($^{3}$He or
demagnetization cryostats), where the time for a single measurement is limited.
In addition, it can be used in moderate magnetic fields $B \leq 10$ T, because
the platform constituents are weakly field dependent.
