Shouldn't enthalpy be constant measured at constant volume? Shouldn't enthalpy be measured at constant volume? Then the work done on and by the gas is 0 meaning that the temperature change is caused solely by heat released or absorbed by the system. You'd be able to calculate
$$\mathrm dQ = \mathrm dT \cdot C_\mathrm s$$ 
(specific heat).
However, since enthalpy is at constant pressure the substance will do or have work done on it and thus there is no easy way to relate the enthalpy change to the change in temperature. Am I mistaken somehow?
Enthalpy is heat flow associated with a constant pressure process.  Here is how:

Start with the familiar first law of thermodynamics for energy change:

$\Delta E=q+w$

$E$=energy

$q$=heat flow into the system

$w$=work done on the system

The work done is rendered thusly:

$w=-\int_\text{start}^\text{end}P\,\mathrm dV$, $P$=pressure, $V$=volume

Pressure is deemed constant so:

$w=-\int_\text{start}^\text{end}P\,\mathrm dV=-P\Delta V=-\Delta(PV)$

And then our first law balance equation becomes:

$\Delta E=q-\Delta(PV)$

$q=\Delta(E+PV)$

So heat flow is the change in a combination of state variables involving energy, pressure and volume.  This combination is what we define as enthalpy and usually label $H$.  Thereby, this enthalpy variable is designed to automatically include (mechanical) work inherent to a constant pressure process.