Widespread flood basalt volcanism and continental rifting in the northeast Atlantic in the early Tertiary period ([tilde operator] 55 Myr ago) have been linked to the mantle plume now residing beneath Iceland *RF 1-5* Although much is known about the present-day Iceland plume [6-9], its thermal structure, composition and position in the early Tertiary period remain unresolved. Estimates of its temperature, for example, range from > 1,600 degrees C in some plume models  to [tilde operator] 1,500 degrees C based on the volume and composition of basaltic crust [10-12]. Several recent studies  have emphasized similarities in the thermal and chemical structure of the Tertiary and present-day plumes to argue for stability of the mantle anomaly, whereas others [12,13] relate variations in basalt volumes and compositions to changes in plume flux. Moreover, some authors [1,2,13] have assumed that the plume was rift-centred for its entire history, whereas others argue that it became ridge-centred only after plate separation [14,15]. Here we report compositional data for [tilde operator] 6,000 metres of flood basalts erupted in east Greenland, close to the inferred plume axis, that we use to constrain the Tertiary plume structure. Rare-earth-element systematics place limits on the pressures and extents of mantle melting and show that the mantle was initially moderately hot ([tilde operator] 1,500 degrees C), but that its temperature declined during flood volcanism. These observations are difficult to reconcile with current plume-head models, and call for important lithospheric control [5,10,16-18] on actively upwelling mantle along the rifted margin.