How can one calculate Load Regulation for a temperature sensor?
The datasheet for the part gives a plot of the typical load regulation as a function of temperature:

I'll take the value to be about 10 \$\mathrm{m}^\circ\mathrm{C}/\mu{}\mathrm{A}\$, since that's a bit higher than the given value over a wide temperature range. The datasheet also specifies that the output &quot;scale factor&quot; (pg 3 of the datasheet) of the TMP37 is 20 mV / degree C. Finally they specify a maximum output current of 50 uA.
\$50 \mu{}\mathrm{A}\times10\mathrm{m}^\circ\mathrm{C}/\mu{}\mathrm{A}\times20\mathrm{mV}/^\circ\mathrm{C}\$ gives about 10 mV error in voltage terms at the maximum specified load current.