Quite truthfully, you can let your yeast starter get as warm as you , they will be perfectly happy up to 98.6ºF or 37ºC, but any thing over that and they will slow their growth rate. When you are making a starter you are not making beer, so don't be too concerned with temperature control. You won't be drinking the starter, so who cares in the higher temps produce some off flavors. When you add the starter to the wort, the yeast need to be as healthy and as happy as they can be, so they can survive as long a possible to ferment your beer fully and correctly, for yeast Beer is a toxic environment . And what ever transfers to primary from the starter, will be cleaned up by a healthy complete fermentation.
You won't get Mutant yeast because you will not me applying any selective pressure on the yeast buy raising the temp in the range that they naturally live. To select for mutant strains of yeast you would need to add some thing that would slow or stop the growth of yeast that Don't have the mutation.