The new and distinct hybrid of Heuchera plant named ‘Appletini’ with cordate foliage of lime green to light chartreuse with a thick silver overlay between the veins on top surface and slight rosy blush underneath in the fall and strong yellowish pink in the spring. Large flowers are deep rich red on compact panicles with some reblooming in the fall. The new plant is vigorous, compact in leaf and flower habit and suitable for use in the landscape en masse, an accent or in containers or cut flowers.