Background: Temperature is an important parameter in studying many important questions in heavy-ion collisions. A thermometer based on the isobaric yield ratio (IYR) has been proposed [Ma et al., Phys. Rev. C 86, 054611 (2012) and Ma et al., ibid., Phys. Rev. C 88, 014609 (2013)].Purpose: An improved thermometer (TIB) is proposed based on the difference between IYRs. TIB obtained from isobars in different reactions will be compared.Methods: The yields of three isobars are employed in TIB. The residual free energy of the three isobars are replaced by that of the binding energy. No secondary decay modification for odd A fragment is used in TIB. Results:The measured fragment yields in the 140A MeV 40,48 Ca + 9 Be ( 181 Ta) and 58,64 Ni + 9 Be ( 181 Ta), the 1A GeV 124,136 Xe + Pb, and the 112,124 Sn + 112,124 Sn reactions have been analyzed to obtain TIB from IMFs. TIB from most of the fragments in the 40,48 Ca and 58,64 Ni reactions is in the range of 0.6 MeV < TIB < 3.5 MeV. TIB from most of the fragments in the 124 Xe and 112,124 Sn reactions is in the range of 0.5 MeV < TIB < 2.5 MeV, while the range is 0.5 MeV < TIB < 4 MeV from most of the fragments in the 136 Xe reaction. In general, for most of the fragments TIB in the 40,48 Ca and 58,64 Ni reactions are very similar (except in the very neutron-rich fragments), and TIB from IMFs in the 124,136 Xe and 112,124 Sn reactions is also similar. A slightly dependence of TIB on A is found.Conclusions: Using the binding energy of the nucleus, TIB can be obtained without the knowledge of the free energies of fragments. In the investigated reactions, TIB from most of the IMFs is low.

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An isoratio method, i.e., the isotopic (isotonic) ratio among three isotopes (isotones), is proposed to study the free energy and temperature effects in the intermediate mass fragments produced in heavy-ion collisions. The parameterizations for the free energy of nucleus at low temperature, which have been proposed in the framework of the density functional theory using the SKM skymre interaction, are adopted to calculate the temperature-dependent free energy of fragment. By analyzing the measured yields of fragments in the 140A MeV 58,64 Ni + 9 Be reactions, it is verified that the free energy in the isoratio is almost the same for different reactions. A temperature-dependent pairing-energy is introduced into the parameterizations for free energy, which reveals that the weakened pairing energy at the low temperature accounts for the weakened or disappearing odd-even staggering in isoratio.

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