So your upset with BMW because of a head gasket failure at 8400 miles? Third owner, after three years. I’d think with any brand you’d be SOL. Many warrantys only last one year. It would not readily seem to be a known flaw in the unit. If it was a manufacturing flaw like a cracked head it should have shown up sooner. The fan coming on too frequent meant you were running hot, Most common cause of overheating is low coolant, who checks that? 310 can have water pump issues with coolant loss. To continue operating a unit when over heating can compromise the head gasket and other component. There is a temperature gauge on the 310 Not a bad idea to monitor if your suspicious.
Stay in touch with your dealer, if you’ve been cooking your bike, there’s much more concern than just a head gasket. They won’t know until start to disassemble. If smart they will inspect cooling system for leaks while there. Depending, you may wish to replace entire motor. Not that much more money for low mileage used or even new with warrant. Have you documented required maintenance on the bike? If cared for properly and it is a manufacturing flaw, there’s a good chance BMW will step up. This is not the first time BMW teamed up with alternate Manufactuner for the smaller bikes. Of course some dealers make less and thus will ignore you. Not a new issue. I think the 310 a well made and innovative unit. Everything seen so far speaks of modern manufacturing and quality control. My biggest peeve so far is the use of hex head screws where I expect a torx as BMW went torx years ago. No big.
This isn’t a bike I’d buy used to be honest. High stressed wee bike, critical maintenance and low initial cost. Not a “forever” bike, best sold or traded in when warranty expires.
Going in with positive attitude will gain far more success than being negative. An open wallet helps too. BMW stands for “Bring Money With” and dealers are used to folks dropping 20k on a bike and thousands on accessories. The only thing cheap on a BMW is the nutter attached to the handlebars. So our wee bikes represent nothing but hassle to them, they all hate Indian production as well, snobbery. It was the same with the Aprilla/Rotax 650 “Funduro”.
So one has to “work” ‘em some. If one does buy used, find a competent independent shop, have the unit inspected prior to purchase. Do not buy without documented maintenance.