Resumen: Aims. We probe the radiatively-efficient, hot wind feedback mode in two nearby luminous unobscured (type 1) AGN from the Close AGN Reference Survey (CARS), which show intriguing kpc-scale arc-like features of extended [O-III] ionized gas as mapped with VLT-MUSE. We aimed to detect hot gas bubbles that would indicate the existence of powerful, galaxy-scale outflows in our targets, HE 0227-0931 and HE0351 + 0240, from deep (200 ks) Chandra observations. Methods. By measuring the spatial and spectral properties of the extended X-ray emission and comparing with the sub kpc-scale IFU data, we are able to constrain feedback scenarios and directly test if the ionized gas is due to a shocked wind. Results. No extended hot gas emission on kpc-scales was detected. Unless the ambient medium density is low (n(H) similar to 1 cm(-3) at 100 pc), the inferred upper limits on the extended X-ray luminosities are well below what is expected from theoretical models at matching AGN luminosities. Conclusions. We conclude that the highly-ionized gas structures on kpc scales are not inflated by a hot outflow in either target, and instead are likely caused by photoionization of pre-existing gas streams of different origins. Our nondetections suggest that extended X-ray emission from an AGN-driven wind is not universal, and may lead to conflicts with current theoretical predictions. Idioma: Inglés DOI: 10.1051/0004-6361/201833424 Año: 2018 Publicado en: Astronomy & astrophysics 618 (2018), A27 [10 pp] ISSN: 0004-6361 Factor impacto JCR: 6.209 (2018) Categ. JCR: ASTRONOMY & ASTROPHYSICS rank: 10 / 69 = 0.145 (2018) - Q1 - T1 Factor impacto SCIMAGO: 2.527 - Space and Planetary Science (Q1) - Astronomy and Astrophysics (Q1)