In a rapidly rotating, electrically conducting fluid we investigate the thermal stability of the fluid in the presence of an imposed toroidal magnetic field and an imposed toroidal differential rotation. We choose a magnetic field profile that is stable. The familiar role of differential rotation is a stabilising one. We wish to examine the less well known destabilising effect that it can have. In a plane layer model (for which we are restricted to Roberts numberq= 0) with differential rotation,U=sΩ(z)1ø, no choice of Ω(z) led to a destabilising effect. However, in a cylindrical geometry (for which our model permits all values ofq) we found that differential rotationsU=sΩ(s)1øwhich include a substantial proportion of negative gradient (dΩ/ds≤ 0) give a destabilising effect which is largest when the magnetic Reynolds numberRm= O(10); the critical Rayleigh number,Rac, is about 7% smaller at minimum than atRm= 0 forq= 106. We also find that asqis reduced, the destabilising effect is diminished and atq= 10−6, which may be more appropriate to the Earth's core, the effect causes a dip in the critical Rayleigh number of only about 0.001%. This suggests that we see no dip in the plane layer results because of theq= 0 condition. In the above results, the Elsasser number A = 1 but the effect of differential rotation is also dependent on A. Earlier work has shown a smooth transition from thermal to differential rotation driven instability at high A [A = O(100)]. We find, at intermediate A [A = O(10)], a dip in theRacvs.Rmcurve similar to the A = 1 case. However, it hasRac≤ 0 at its minimum and unlike the results for high A, larger values ofRmresult in a restabilisation.