Given that the temperature versus time engine is
1.2t=Tm
Temperature of the environment is 15=Te
Constant k=0.8
It is known that the rate of the cooling is define by

dT/dt = -k(T-Te)+Tm

Also known that the speed of the robot is 25m/s And the starting temparture of the engine is 35.

We need to find the Differential Equations for the road founded in the last question for Each Δt=0.1

This is a standard DE for cooling of a body, with the exception of the Tm term. You have left out some critical information. What is the definition of Tm, what does a robot have to do with anything, and how does the velocity of the robot play into it?