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In high-resolution adiabatic scanning calorimetry (ASC) experiments, data for the temperature dependence of the specific enthalpy, h(T), and of the specific heat capacity, c(p)(T), are simultaneously obtained, from which the order of the phase transition and critical behaviour can be evaluated. ASC was applied to study the nematic to ferroelectric nematic phase transition (N-N-F) in the liquid crystal molecule 4-[(4-nitrophenoxy)carbonyl]phenyl 2,4-dimethoxybenzoate (RM734). The N-N-F was found to be very weakly first order with a latent heat Delta h = 0.115 +/- 0.005 J/g. The pretransitional specific heat capacity behaviour is substantially larger in the high-temperature N phase than in the low-temperature N-F phase. In both phases the power-law analysis of c(p)(T) resulted in a critical exponent alpha = 0.50 +/- 0.05 and amplitude ratio A(NF)/A(N) = 0.42 +/- 0.03. The very small latent heat and the value of alpha indicate that the N-N-F transition is close to a tricritical point. This is confirmed by a value of the order parameter exponent beta approximate to 0.25, recently obtained from electric polarisation measurements. Invoking two-scale-factor universality, it follows from the low value of A(NF)/A(N) ratio that the size of the critical fluctuations is much larger in the N-F phase than in the N phase.