  The close encounter of a white dwarf (WD) with a black hole (BH) could result
in the tidal disruption of the WD. During this encounter, the WD can undergo a
thermonuclear explosion due to its tidal compression, resulting in an optical
transient similar to a Type Ia supernova (SN Ia), hereafter a Ia-TDE.
Nevertheless, this will only be physically observable if the BH is $\lesssim
10^5$M$_\odot$. Finding a Ia-TDE would therefore imply the discovery of an
intermediate mass black hole (IMBH) $\lesssim 10^5$ M$_\odot$. Here, we search
the entire Zwicky Transient Facility (ZTF) alert stream for the elusive
Ia-TDEs. We restrict our search to nuclear transients in dwarf galaxies, the
likely sites for IMBHs, and find a total of six possible nuclear Ia-TDE
candidates. We find SN\,2020lrt to be the most likely Ia-TDE candidate, thanks
to its strong resemblance to light curve and spectroscopic models of Ia-TDEs.
We measure the stellar masses of the dwarf galaxies hosting these transients to
be $\lesssim 10^{9}$M$_\odot$; if confirmed to harbor BHs, these would prove
the existence of IMBHs in some of the lowest-mass galaxies known. Additionally,
we searched for off-nuclear Ia-TDEs, but were unable to find more robust
candidates in the outskirts of galaxies than in their nuclei. This supports the
hypothesis that the nuclear Ia-TDEs candidates are WDs tidally compressed by
IMBHs in the cores of galaxies, as opposed to a class of transient that can
happen anywhere in a galaxy. We have laid the groundwork to systematically
search for Ia-TDE candidates in existing and future time-domain surveys. Rapid
characterization of their nature will result in not only the confirmation of a
Ia-TDE, but also the unambiguous discovery of bonafide IMBHs.
