The photopyroelectric technique has been adopted to study the critical behaviour associated with the thermal parameters over smectic A - nematic (S-A-N) phase transition in both 4-n-nonyl-4'-cyanobiphenyl (9CB) and 4-n-pentylphenylthiol-4'-noctyloxythiolbenzoate ((8) over bar S5) through the simultaneous determination of the specific heat (e) as well as of transport parameters like thermal diffusivity (D) and thermal conductivity (k). In the case of 9CB, the critical exponent of specific heat agrees with the value of 0.5 expected from the theory of mean field tricritical behaviour. On the other hand, for (8) over bar S5 the values of critical exponent is close to the one of 3D XY-like second order phase transition, in agreement with earlier investigations. In all cases the thermal conductivity showed no anomaly.