Remove the thermostat cover and thermostat after draining the coolant.
If the studs still have some length projecting out of the head you can weld nuts onto the studs and with the studs still hot from the welding they will probably unscrew.
If not, you will need to cut the studs off flush with the head and drill them out. The fit Heli-Coil thread repair inserts - the size is 1/4" UNC - and fit new studs available from all the main Mini Spares vendors.
It is a very common problem. If it happens to me I usually take the head off and do the job 'on the bench' as it's easier to drill out and Heli-Coil using a pillar drill. If you don't have the equipment you can take the head to a local machine shop. Be sure to fit 1/4" UNC Heli-Coils, not 1/4" UNF.
Do not use stud extractors as, if/when the extractor breaks it is just one hell of a job doing the repair (been there, done that).
Edited by Cooperman, 21 November 2013 - 11:14 PM.