When do winds gets stronger?
Your question is a bit confusing, but there is a strong connection between temperature and wind,in their spatial gradiant I would say, however, instead of temporal differences.

Imagine winds are only driven by changes in pressure (higher temperatures -> lower pressure and vice versa). Imagine there are two surface areas with different temperatures (say some frozen lake and a nice grass field in the sun nearby). Therefore the horizontal pressure gradient (due to horizontal temperature gradient) would force the existence of wind, blowing from the High to the Low pressure zones. 

Now imagine another situation where there is no horizontal gradient (differences) of temperature nor pressure. The surface is homogeneous. Now imagine all the homogenous surface gets warmer at the same rate, but still remains homogeneous). There would be no reason, thus, for stronger winds (apart from molecular-scale phenomena due to warming, but I believe is not the focus here).

To summarize: winds driven by temperature differences do get stronger if temperature differences spatially increase. A high temperature, alone, does not say much and is way to vague to relate to what you ask.

You could also think of Antartica: very cold and high speed winds. Just to give a hint of how more complicated the relation between temperature and wind may be.