The Type Ia supernova (SN Ia) SN 2000cx was one of the most peculiar transients ever discovered, with a rise to maximum brightness typical of a SN Ia, but a slower decline and a higher photospheric temperature. Thirteen years later SN 2013bh (aka iPTF13abc), a near identical twin, was discovered and we obtained optical and near-IR photometry and low-resolution optical spectroscopy from discovery until about 1 month past r-band maximum brightness. The spectra of both objects show iron-group elements (Co II, Ni II, Fe II, Fe III, and high-velocity features [HVFs] of Ti II), intermediate-mass elements (Si II, Si III, and S II), and separate normal velocity features (~12000 km/s) and HVFs (~24000 km/s) of Ca II. Persistent absorption from Fe III and Si III, along with the colour evolution, imply high blackbody temperatures for SNe 2013bh and 2000cx (~12000 K). Both objects lack narrow Na I D absorption and exploded in the outskirts of their hosts, indicating that the SN environments were relatively free of interstellar or circumstellar material and may imply that the progenitors came from a relatively old and low-metallicity stellar population. Models of SN 2000cx, seemingly applicable to SN 2013bh, imply the production of up to ~1 M_Sun of Ni-56 and (4.3-5.5)e-3 M_Sun of fast-moving Ca ejecta.
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