Planets form in discs of gas and dust around stars, and continue to grow by accretion of disc material while available. Massive planets clear a gap in their protoplanetary disc, but can still accrete gas through a circumplanetary disc. For high enough accretion rates, the planet should be detectable at infrared wavelengths. As the energy of the gas accreted on to the planet is released, the planet surroundings heat up in a feedback process. We aim to test how this planet feedback affects the gas in the coorbital region and the accretion rate itself. We modified the 2D code FARGO-AD to include a prescription for the accretion and feedback luminosity of the planet and use it to model giant planets on 10 au circular and eccentric orbits around a solar mass star. We find that this feedback reduces but does not halt the accretion on to the planet, although this result might depend on the near-coincident radial ranges where both recipes are implemented. Our simulations also show that the planet heating gives the accretion rate a stochastic variability with an amplitude Delta M-p similar to 0.1M(p). A planet on an eccentric orbit (e = 0.1) presents a similar variability amplitude, but concentrated on a well-defined periodicity of half the orbital period and weaker broad-band noise, potentially allowing observations to discriminate between both cases. Finally, we find that the heating of the co-orbital region by the planet feedback alters the gas dynamics, reducing the difference between its orbital velocity and the Keplerian motion at the edge of the gap, which can have important consequences for the formation of dust rings.