Flow-induced vibration (FIV) of the modified single-cylinder with a change in corner radius has been investigated in a laminar flow regime with Re = 100 and Pr = 0.7. The corner radius (r: corner radius, :R cylinder characteristic length) is changed from 1 to 0 and two angles α; 0° and 45° are used. The Cylinder is elastically supported with heating at a constant temperature at the boundaries. Vibrations are restricted to the transverse direction. Computation is carried out with a fixed mass ratio m* = 10 and varying reduced velocity Ur = 2 ∼ 8. The two-dimensional incompressible Navier-Stokes equations and energy equations are coupled together. Navier stokes equation used with FIV equation of elastically supported cylinder to have flow solutions. Lock-in synchronization can be observed at Ur = 5 and Re = 100 at r* = 1 which leads to severe vibration and maximum vibrational amplitude A/D while amplitude modulation has been observed at Ur = 5 for the square cylinder. Based on the mode of vibration whole study has been divided into 4 ranges of vibration. Mode-I, where the amplitude is very low; Mode-II, fluctuating amplitude known as hysteresis (Beating); Mode-III; amplitude is at the maximum because of lock-in synchronization; Mode-IV, normal vibrational amplitude. Different modes are compared with the change in Ur, r* and α. The effect of Ur is visible on the Nusselt number as more vibration leads to a high value of averaged Nusselt number NuAvg. Vortex shedding is changed from C(2S) to 2S as the corner radius is modified. Results give a deep insight into heat transfer getting changed by changing three different parameters and will make a base for future study of tube bundles in heat exchangers with FIV.