This dissertation discusses the hydrography of hydrothermal plumes and the problem of measuring the flux of heat from the Main Endeavour hydrothermal vent field (MEF) on the Endeavour segment of the Juan de Fuca ridge in the northeast Pacific. Primary data are from an underwater vehicle called Autonomous Benthic Explorer (ABE), a lowered CTD, and 2 current meter moorings. Context for the estimation of MEF heat flux is established in Chapter~\ref{ch:power} through motivating questions, definition of terminology, re-examination of plume theory, and review of past heat flux measurements at the MEF. A new correction factor is derived to relate plume heat flux calculated with isohaline temperature anomalies to source heat flux. Chapter~\ref{ch:flowmow} presents the setting and methodology of the study, and an analysis of hydrography and currents near the MEF. The main hydrographic observation is high variability near the MEF, where hydrothermal plumes vary on scales as short as 10--50\,m and 10--60\,min. On average, fluid is warmer near the center of hydrothermal activity, especially within the axial valley. Another major result is that oscillatory currents change from multidirectional above the ridge to rectilinear within the axial valley \cite{thomson+03}. A perisistent northward mean flow of 2-5\,cm/s, observed within the axial valley near the MEF, is aligned with the rectilinear oscillations ($\sim$5\,cm/s amplitude), while the southwestward mean flow of 5-10\,cm/s observed above the ridge is only intermittently parallel to the multidirectional oscillations ($\sim$5\,cm/s amplitude). Since the problem of estimating heat flux is distinct in these 2 types of flow, it is addressed separately within the axial valley (Chapter~\ref{ch:lower}) and above the ridge (Chapter~\ref{ch:upper}). In both cases, a mathematical model of advection and diffusion is used to simulate plume distributions and analyze heat flux statistics. The \emph{horizontal heat flux within the axial valley} through vertical control surfaces extending from the sea floor to $\sim$100\,m above bottom (mab) is $\sim$65\,MW, based on the warmth of the north end of the MEF relative to the south end and the northward mean flow. The model indicates the standard deviation of this mean horizontal flux is $\sim$100\,MW. The \emph{vertical heat flux} through a horizontal surface near 100\,mab is 550$\pm$100\,MW, derived from vertical velocity and hydrography measured in rising plumes \cite{stahr+03}. This vertical flux, previous measurements of source flux, and the horizontal flux together imply that heat flux partitioning between focused and diffuse sources is $\sim$6:1. %confirming the results of \cite{lavelle+01} and further questioning This ratio contradicts the prevalent view that diffuse sources account for 90\% of the heat flux at vent fields. An additional implication is that $\sim$ %80\% 25\% of diffuse heat flux is entrained by focused plumes. The \emph{horizontal heat flux above the ridge} through vertical control surfaces extending from 100--400\,mab is 315$\pm$651\,MW. This mean value is consistent with the vertical flux estimate. Past estimates of flux in plumes are higher because they are not net fluxes and likely include contributions from multiple vent fields.