This paper deals with the control of the temperature in non-isothermal stirred-tank reactors involving M (M greater-than-or-equal-to 1) chemical reactions. The proposed control algorithm is an input-output linearization controller which accounts for the well-known process nonlinearities. The control scheme is also adaptive in order to deal with the parameter uncertainty : in particular it is shown how to include explicit on-line estimates of the M activation energies within the adaptive linearizing controller. The performance of the control law is illustrated in simulation.