= Solution
<Temperature> describes thermal state and determines the direction of spontaneous <heat transfer>. A quantity of <heat> is energy transferred because of a temperature difference. It depends on the process and is measured in energy units; it is not another name for temperature. Equal heat inputs need not produce equal temperature rises in different masses or substances.
For a specified process, the <specific heat capacity> is
$$
\boxed{c=\frac1m\frac{\delta Q}{dT}.}
$$
Over a modest range with nearly constant $c$ and no phase change, $Q=mc\Delta T$. For a gas the constraint matters: <heat capacity at constant pressure> and <heat capacity at constant volume> generally differ because expansion can do work.
In <method-of-mixtures calorimetry>, a body of known mass $m_s$ at $T_s$ is transferred into water of mass $m_w$ at $T_w$ in a calibrated <calorimeter> initially also at $T_w$. If the final uniform temperature is $T_f$, the vessel and immersed fittings have heat capacity $C_{\rm cal}$, and losses are negligible,
$$
m_sc_s(T_s-T_f)=(m_wc_w+C_{\rm cal})(T_f-T_w).
$$
Thus
$$
\boxed{c_s=\frac{(m_wc_w+C_{\rm cal})(T_f-T_w)}
{m_s(T_s-T_f)}.}
$$
Stirring, quick transfer, a lid, a temperature-time record and allowance for surrounding heat exchange improve the inference. Ignoring the calorimeter's heat capacity systematically misattributes part of the energy uptake.
An alternative is <electrical calorimetry>: measure $E=\int VI\,dt$ supplied to a heater and compare the temperature rise with a blank or separately calibrated vessel. At nearly constant properties, $E=(mc+C_{\rm cal})\Delta T+Q_{\rm loss}$. An <ice calorimeter> instead measures the mass melted at a known phase-change temperature, using $Q=m_{\rm melt}L_f$ with appropriate corrections. Steam condensation similarly uses latent heat. These methods infer transferred energy from different measurable effects; a thermometer reading alone does not measure a quantity of heat.
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