You'd think in theory a quad core system should be able to handle a dual core program fine, since both are designed with multiple cores in mind. In practice I'd think it should be much less likely than a single threaded program having problems on a multi core system, but we are talking about computers here, so I wouldn't be terribly shocked if a dual core program did have issues on a quad core CPU.
It couldn't hurt to try setting the affinity to specific cores.
