Answer
The increase in thermal energy = $-$ work done by kinetic friction = 560 J
Work Step by Step
Kinetic friction acting on the block, $f_{k}=\mu_{k} N=\mu_{k} (mg+Fsin\theta)$
So, work done by kinetic friction in displacement d of the block, $W_{f_{k}}=f_{k}d cos180^{\circ}$
$W_{f_{k}}=-0.20\times (27 \times9.8+71\times sin\ 32^{\circ}) \times 9.2=-560 J$
Here negative sign indicates that energy is lost in form of heat.
