The density of water as a function of temperature has a maximum around 4 degrees Celsius, so "hot" water is actually lighter than "cold" water. The mass defect is a very small quantity for most binding energies (as you devide by $c^2$).
The mass defect of the proton and the neutron, each consisting of 3 quarks, is about 99% of their rest mass, the mass defect due to the binding energy for most nuclei is on the order of a few percent, while the mass defect due to electronic binding energy is on the order of $10^{-8}$ (one millionth of a percent). You can imagine that vibrational, rotational and translational energy have even smaller mass defects that are very hard to measure.
Let us - just for fun - assume that we could measure a 0.1% increase in the density of 1L water solely due to an increase in kinetic energy of the water molecules. Ignoring the normal temperature behavior of the density of water, this corresponds to an energy of
$\Delta E=0.1\% \cdot m_{\text{H}_2\text{O}} \cdot n \cdot c^2
\\\qquad=0.001\cdot 18 \text{ g mol}^{-1}\cdot 55.6\text{ mol L}^{-1}\cdot 9\cdot 10^{16} \text{m}^2\text{ s}^{-2}\\\qquad\approx 9\cdot10^{13}\,\text{J L}^{-1}$
Converting this kinetic energy to a temperature we get something on the order of $10^{13}$ $^\circ\!$C!
You can also try to calculate the increase in mass for water at room temperature and will see this is a very tiny fraction of the rest mass.
