We present a method for measuring changes of enthalpy to discriminate the contribution due to the latent heat from that due to the temperature dependence of the specific heat near the transition point. The same conduction calorimeter, whose sensor is formed by two identical heat fluxmeters, determines the specific heat and the heat flux exchanged by the sample when its temperature changes at constant rates as low as 0.1 K h(-1). The method is applied to the KMnF3 crystal, which undergoes a first-order transition close to a tricritical point at 186 K, and the doped crystal KMn0.96Ca0.04F3, whose transition becomes second-order. The latent heat of pure KMnF3 is evaluated to be 0.129 +/- 0.002 J g(-1). Although the thermal analysis signal of KMn0.96Ca0.04F3 crystal presents a peak, it is entirely due to the contribution of the specific heat, which indicates that the transition is second-order.