We present new Spitzer/IRS spectra of two hot R Coronae Borealis (RCB) stars, one in the Galaxy, V348 Sgr, and one lying in the Large Magellanic Cloud, HV2671. These two objects may constitute a link between the RCB stars and the late Wolf-Rayet ([WCL]) class of central stars of planetary nebulae (CSPNe), such as CPD -56° 8032, that has little or no hydrogen in their atmospheres. HV2671 and V348 Sgr are members of a rare subclass that has significantly higher effective temperatures than most RCB stars, but shares the traits of hydrogen deficiency and dust formation that define the cooler RCB stars. The [WC] CSPN star, CPD -56° 8032, displays evidence of dual-dust chemistry showing both polycyclic aromatic hydrocarbons (PAHs) and crystalline silicates in its mid-IR spectrum. HV2671 shows strong PAH emission but no sign of having crystalline silicates. The spectrum of V348 Sgr is very different from that of CPD -56° 8032 and HV2671. The PAH emission seen strongly in the other two stars is not present. Instead, the spectrum is dominated by a broad emission centered at about 8.2 μm. This feature is not identified with either PAHs or silicates. Several other cool RCB stars, novae, and post-asymptotic giant branch stars show similar features in their IR spectra. The mid-IR spectrum of CPD -56° 8032 shows emission features that may be associated with C60. The other two stars do not show evidence of C60. The different nature of the dust around these stars does not help us in establishing further links that may indicate a common origin. HV2671 has also been detected by Herschel/PACS and SPIRE. V348 Sgr and CPD -56° 8032 have been detected by AKARI/Far-Infrared Surveyor. These data were combined with Spitzer, IRAS, Two Micron All Sky Survey, and other photometry to produce their spectral energy distributions (SEDs) from the visible to the far-IR. Monte Carlo radiative transfer modeling was used to study the circumstellar dust around these stars. HV2671 and CPD -56° 8032 require both a flared inner disk with warm dust and an extended diffuse envelope with cold dust to fit their SEDs. The SED of V348 Sgr can be fit with a much smaller disk and envelope. The cold dust in the extended diffuse envelopes inferred around HV2671 and CPD -56° 8032 may consist of interstellar medium swept up during mass-loss episodes.