ABSTRACT We studied the transient Galactic black hole candidate MAXI J0637−430 with data from Insight-HXMT, Swift, and XMM–Newton. The broad-band X-ray observations from Insight-HXMT help us constrain the power-law component. MAXI J0637–430 is located at unusually high Galactic latitude; if it belongs to the Galactic thick disc, we suggest a most likely distance ≲7 kpc. Compared with other black hole transients, MAXI J0637–430 is also unusual for other reasons: a fast transition to the thermal dominant state at the start of the outburst; a low peak temperature and luminosity (we estimate them at ≈0.7 keV and ≲0.1 times Eddington, respectively); a short decline time-scale; a low soft-to-hard transition luminosity (≲0.01 times Eddington). We argue that such properties are consistent with a small binary separation, short binary period (P ∼ 2 h), and low-mass donor star (M2 ∼ 0.2 M⊙). Moreover, spectral modelling shows that a single disc blackbody component is not a good fit to the thermal emission. Soft spectral residuals, and deviations from the standard $L_{\rm disc} ∝ T_{\rm in}^4$ relation, suggest the need for a second thermal component. We propose and discuss various scenarios for such component, in addition to those presented in previous studies of this source. For example, a gap in the accretion disc between a hotter inner ring near the innermost stable orbit, and a cooler outer disc. Another possibility is that the second thermal component is the thermal plasma emission from an ionized outflow.