We studied the dynamics of the Heat Shock Response (HSR) mechanism, and the persistence of a injury-protected state in the cell following the shocks, known as thermotolerance. A series of double shock experiments were performed on Chinese Hamster Ovary (CHO) cells, tracking the dynamics of some components of HSR pathway (the Hsp70 protein level and Hsp70 mRNA transcription rate). The main features of HSR dynamics were well reproduced by a simplified model of the chemical reaction pathways governing the HSR. In particular, the thermotolerance phenomenon could be well characterized by introducing a shock-dependent switch in mRNA halflife, that can be interpreted as a sort of primitive memory at the mRNA level.