It really depends upon how long she sits and spins, and where. If she were to find a current and sit and spin over it, the intensity would go up. If she were to sit and stir the water elsewhere, ultimately the water would cool down.

Looking at the IR4 loop.... IF that is an eye developing (not confident that it is yet), the storm is beginning to move northward, it appears to me, and is a LOT stronger than 70 mph (you typically don't see an eye on a cat 1 hurricane). Looking closely, though... I think the LLC is south of the eye feature. Still, it looks like it will get pulled north sooner rather than later - going closer to the tip of Cuba than the Yucatan peninsula.

Update: "Eye" feature was short-lived. Next IR4 image showed VERY cold cloud tops (the black things again)... but still looks to me like it's moving NW or NNW (there is definately a west component, and if the LLC is under that black area, there is a north component too).