Sorry, I've no idea about how easy (or otherwise) it is to replace a thermostat but I'd ask you to reconsider your diagnosis of the fault. If you can hear a hum it suggests that the fridge-freezer is trying to cool the warm air inside it. (i.e. the thermostat is in the 'on' position, as it should be if it contains warm air). Since it's obviously failing in this task, it suggests that the coolant has leaked out.
All new electrical appliances should be expected (irrespective of any guarantee) to work for a minimum of 6 years. If a device fails within that period due to an inherent fault (e.g. poor workmanship or the use of poor quality components) the law requires the retailer (not the manufacturer) to remedy the fault by providing a repair or replacement. Since more than 6 months have passed from the date of purchase, there is no longer an automatic legal assumption that the problem must be due to an inherent fault. You're required to show, based upon the balance of probabilities, that an inherent fault is the most likely cause of the problem.
Contact the retailer and state that your fridge-freezer has failed. Challenge the retailer to suggest any other cause than an inherent fault. When he can't do so, demand a (free) repair or replacement, under your statutory rights.
Chris



