The distribution of eccentricities of warm giant exoplanets is commonly explained through planet--planet interactions, although no physically sound argument favours the ubiquity of such interactions. No simple, generic explanation has been put forward to explain the high mean eccentricity of these planets. In this paper, we revisit a simple, plausible explanation to account for the eccentricities of warm Jupiters: migration inside a cavity in the protoplanetary disc. Such a scenario allows to excite the outer eccentric resonances, a working mechanism for higher mass planets, leading to a growth in the eccentricity while preventing other, closer resonances to damp eccentricity. We test this idea with diverse numerical simulations, which show that the eccentricity of a Jupiter-mass planet around a Sun-like star can increase up to 0.4, a value never reached before with solely planet--disc interactions. This high eccentricity is comparable to, if not larger than, the median eccentricity of warm Saturn- to Jupiter-mass exoplanets. We also discuss the effects such a mechanism would have on exoplanet observations. This scenario could have strong consequences on the discs lifetime and the physics of inner disc dispersal, which could be constrained by the eccentricity distribution of gas giants.
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