Factors that influence the kinetics of an irreversible exothermic reaction I'm trying to understand what are the main factors that influence the reaction rate of an irreversible exothermic reaction. 

I think these could be the main factors: 


chemical nature of the reagents and their concentration;
nature of the solution (homogeneous or heterogeneous)
presence of catalysts 
temperature. 


(Let me know if I missed some factors or added one or two that had nothing to do with what I'm looking for.)

But I struggle understanding how the temperature influences an exothermic reaction. I can't use Le Chatelier's principle since the reaction is not reversible, so how do I know what is the effect of (for example) an increased temperature on such reaction? 

I'm prone to think that an increased temperature will bring more products, but then again I'm not so sure since is an irreversible reaction.
I assume by kinetics you mean the rate of the reaction (i.e. how fast it happens), in which case the factors you mention are fine. 

Regarding the temperature: the rate constant and therefore the reaction rate at a given concentration always increases with temperature as you can see in the Arrhenius equation. The fact the the reaction is exothermic means that it releases heat which, in the case where no adequate temperature control is applied (such as an ice bath), will increase the temperature of the solution and therefore the rate of the reaction releasing even more heat and so on, resulting in a runaway exotherm. This is the reason why exothermic reactions must be well temperature controlled especially when performed in large scale.

If your reaction was reversible, then heating it would not only accelerate the reaction (both forwards and backwards at equilibrium) but also shift the equilibrium towards the reactants.