Single plagioclase paleointensity experiment has been an excellent tool to reliably estimate ancient geomagnetic field intensity. Although transparent plagioclases with magmatic nanophase magnetites have shown their potential for paleointensity estimation, in most cloudy plagioclases with exsolved magnetites, the problems of strong anisotropy as rod-shape magnetites, the hyperbolic tangential saturation of thermoremanence (TRM), and slow cooling of host plutons need to be addressed. In this paper, we propose experimental schemes to address these problems with considerations of error estimation and uncertainty for paleointensity experiments on exsolved magnetite. First, in order to experimentally check the effect of the hyperbolic tangential saturation of TRM, we performed Thellier simulation experiments using laboratory total TRM as simulated natural remanence (NRM). Single cloudy plagioclases were sampled from early Cretaceous granite in the Kitakami massif, Northeast Japan. We designed the experiment where the total TRM and the partial TRMs in the Thellier experiments were acquired under different field intensities. For these experiments, correction for hyperbolic tangential TRM acquisition yielded precise field intensity estimations. Next, Thellier experiments on NRM of the crystals from the same granite were performed as a demonstration of correction schemes for both magnetic anisotropy and hyperbolic tangential TRM acquisition. Precise determination of anisotropy tensor seems to be the major challenge for single plagioclase paleointensity estimation with exsolved magnetite.