Basically, just turn away from the star (just enough, not all the way), keeping the destination dot (i.e. your next system) in the space compass solid but off-centre, then accelerate ensuring your temperature drops, watch the temperature drop to a safe level (below 50deg for me) then you can start your FSD charge and turn, pitch, whatever to bring your destination into centre of HUD - count finishes, jump starts, zero throttle.
Rinse and repeat.
- - - Updated - - -
If this is happening then you are arriving at the star with some throttle set and so have been dropped out of supercruise. You will overheat as you engage the FSD as you are so close to the star, the trick is to either fire off a heatsink as you charge or accept the minor heat damage and repair it on your next docking.
To avoid having this happen, ALWAYS zero your throttle as the hyperdrive engages - I do it when the countdown finishes - that way you always arrive at the star with min speed and should never be dropped from supercruise. (It has happened to me a few times with close binaries but it is very very rare.)