Strobe + Speedlight: Matching light quality

I am often times working with a portable setup and mixing speedlights with strobes. Usually I have a strobe as a key and use speedlights for hair lights and for the background. While this works, there is a noticeable difference in light quality. Would a piece of gel warm up the speedlight enough? Would it become too warm?

Here's an example of what I'm talking about:

A 1/4 CTO gel should warm it just enough to match your strobe.

If you are shooting the strobe through a diffusion panel on a softbox that is also affecting the light color.

As Jim says CTO is the answer. There are speedlite gel packs available that have a range from 1/8th to full. They are also useful for balancing with room lights. The original intent.