Can antimatter-matter collisions generate heat? We have a project at school to develop an idea about how we can generate electricity.
My question is: do collisions between matter and antimatter particles generate heat, so that one could harvest it using turbines?
 A: Not at first, but usually eventually. 
You should read the Wikipedia article on Annihilation, which is the name of the phenomenon of a particle's colliding with its anitparticle. 
Particles and antiparticles have opposite-signed, equal magnitude quantum numbers (such as spin and parity to name two). Collisions must conserve these quantum numbers, so the peculiar, special case of all quantum numbers summing to nought means that any other set of particles with zero sum quantum numbers can emerge from the collision, as long as total energy and momentum are conserved by the collision.
The most common products, though, are pairs of photons with opposite spins, particularly with low energy particles. These are very high frequency photons - gamma rays. Gamma particles are quite penetrating - they can travel deep into matter before being absorbed. 
At this point, the absorbed gammas add to the heat of the absorbing matter.
A: When a particle collides with its antiparticle, all of the mass in both is converted into electromagnetic energy (usually high energy gamma radiation).
Whilst it is certainly possible to then convert this gamma radiation into heat so as to drive a turbine, it may be also possible to convert gamma radiation directly into electricity using a special type of 'nuclear solar panel'.
