  We consider a binary stellar system, in which a low-mass, of 0.6 Msun,
carbon-oxygen white dwarf (WD) mergers with a degenerate helium core of 0.4
Msun of a red giant. We analyse the outcome of a merger within a common
envelope (CE). We predict the observational properties of the resulting
transient. We find that the double detonation of the WD, being a pure
thermonuclear explosion and embedded into the hydrogen-rich CE, has a light
curve with the distinct plateau shape, i.e. looks like a supernova (SN) Type
IIP, with a duration of about 40 days. We find five observed SNe IIP: SN
2004dy, SN 2005af, SN 2005hd, SN 2007aa, and SN 2008bu, that match the V-band
light curve of our models. Hence, we show that a thermonuclear explosion within
a CE might be mistakenly identified as a SN IIP, which are believed to be an
outcome of a core-collapse neutrino-driven explosion of a massive star. We
discuss a number of diagnostics, that may help to distinguish this kind of a
thermonuclear explosion from a core-collapse SN.
