Kinetic temperature of massive star-forming molecular clumps measured with formaldehyde IV. The ALMA view of N113 and N159W in the LMC

We mapped the kinetic temperature structure of two massive star-forming regions, N113 and N159W, in the Large Magellanic Cloud (LMC). We have used $\sim$1\hbox{$\,.\!\!^{\prime\prime}$}6\,($\sim$0.4\,pc) resolution measurements of the para-H$_2$CO\,$J_{\rm K_ aK_c}$\,=\,3$_{03}$--2$_{02}$, 3$_{22}$--2$_{21}$, and 3$_{21}$--2$_{20}$ transitions near 218.5\,GHz to constrain RADEX non-LTE models of the physical conditions. The gas kinetic temperatures derived from the para-H$_2$CO line ratios 3$_{22}$--2$_{21}$/3$_{03}$--2$_{02}$ and 3$_{21}$--2$_{20}$/3$_{03}$--2$_{02}$ range from 28 to 105\,K in N113 and 29 to 68\,K in N159W. Distributions of the dense gas traced by para-H$_2$CO agree with those of the 1.3\,mm dust and \emph{Spitzer}\,8.0\,$\mu$m emission, but do not significantly correlate with the H$\alpha$ emission. The high kinetic temperatures ($T_{\rm kin}$\,$\gtrsim$\,50\,K) of the dense gas traced by para-H$_2$CO appear to be correlated with the embedded infrared sources inside the clouds and/or YSOs in the N113 and N159W regions. The lower temperatures ($T_{\rm kin}$\,$<$\,50\,K) are measured at the outskirts of the H$_2$CO-bearing distributions of both N113 and N159W. It seems that the kinetic temperatures of the dense gas traced by para-H$_2$CO are weakly affected by the external sources of the H$\alpha$ emission. The non-thermal velocity dispersions of para-H$_2$CO are well correlated with the gas kinetic temperatures in the N113 region, implying that the higher kinetic temperature traced by para-H$_2$CO is related to turbulence on a $\sim$0.4\,pc scale. The dense gas heating appears to be dominated by internal star formation activity, radiation, and/or turbulence. It seems that the mechanism heating the dense gas of the star-forming regions in the LMC is consistent with that in Galactic massive star-forming regions located in the Galactic plane.