[Spatika]

Does an exothermic reaction increase the temperature of the 'system' or 'surroundings?
An exothermic reaction is one that releases heat energy, so shouldn't that mean that it increases the temperature of the surroundings, rather than that of the system?
 
But my book says that when you mix two liquids, and they result in a cooler solution, the reaction is endothermic. If the resulting solution is cooler, wouldn't it mean that the reaction gives out heat as one of its products, to the surroundings? 

[MrTeo]

First of all energy changes happen at a molecular level (they are caused by the breaking of some bonds and the forming of others: reaction enthalpies can be roughly evaluated calculating the changes in bond energy) so the energy is taken from (or given to) the solution itself. Obviously the reaction can be exothermic enough to cause the heating of the surroundings too (try to mix NaOH and vinegar in a bowl and you'll feel the heat released) but this is simply caused by the conduction of a part of the energy released through the container.

[ContinuousProcess]

If it's colder than everything around it, everything around it will warm it up.

It's not radiating heat, it's absorbing it.