my laptop crashes around every half an hour, it just turns itself off. I think it may be to do with overheating, as it gets very hot very fast. Is there anything I can do to find out what the problem is and fix it, idealy without having to purchase any new hardware etc.

What is the exact make & model?

Is this a new problem? Was it working OK before?

Also: look in your Event viewer: rt. click My Computer then click Manage then Event Viewer.
Or: Administrative Tools/Event Viewer or Start/Run/ eventvwr
Open the system as well as the application tabs & look for X errors. Click error line for details.
Post back the source & event id especially of errors that seem to coincide with a crash.

Also check the Device Manager: RT click My Computer then click Manage then Device Manager or go to start/run/ devmgmt.msc for any "!"

Can you locate the heat source? Hard drive? Graphics area?

Laptop coolers are made. Essentially they add a half inch air space on the bottom; some have small fans built in.