Yes, the Eberspacher Easystart Pro controller would be an ideal upgrade replacement for a faulty 802 controller. It also has added functionality to utilise it's integrated temperature sensor to regulate heater output as you require ( needs a one-time selection within the initial installation config of the controller)
Unfortunately it is unlikely to just swap out with the 802, they do not share the same electrical plug type. We would need to learn alittle more ab out your existing wiring set up to advise the easiest simplest method to connect up the Easystart Pro, shouldn't be too difficult.
Perhaps email some photos of your electrical connections to sales@butlertechnik.com for further help on this. Mention this message thread if you do please, just so we can keep track of your enquiry
Thanks