Our deterministic model is the best option to represent our system because we assume that all the variables behave continuously and obey kinetic rules, in other words, we don´t take account other variables that are going to disturbe our system. Also, it is perfect to model our equations that represent the production of mRNA and proteins of cI, Vip3Ca3, and GFP of each respective part of our system and have something precise with the parameters we get and the graphics that represent the behavior of the concentration of the new substances produced by E.coli. The probability equation it is still in development but we are trying to figure out how the thermosensor can affect the proteins translation process, besides the variable of temperature that control our system. We have to understand that a Math model is never going to be a perfect representation, they try reach the closest to reality they could, adding new variables and parameters, including noise and new equations approach them being a better model. Our modeling is a way to understand how are the actions and behavior of the genetic system we introduced in the genome of E.coli; and some assumptions in the experimentation of our proyect.