The results of computer simulation of a new one-dimensional carbon structure - chains consisting of C20 carbinofullerenes linked by carbon atoms are presented. Their bond energy values are determined. Their thermal stability is studied by the method of molecular dynamics. The stability of chains to tension was also investigated and compared with the stability of chains of C20 carbynofullerenes without intermediate carbon atoms. It has been shown that the preferred channel of thermal decay is the fusing of neighboring carbynofullerenes, and the deformation channel is the separation of the extreme carbinofullerene from the chain. The ultimate strains of chains and also the temperature dependence of their lifetime until the time of decay are determined. The values of activation energies and frequency factors of the decay process in the Arrhenius law are found.