Agree with @Ivt - "not normal".
Batteries getting too hot to touch are dangerous.
Is the mouse showing any signs of damage? Which specific model mouse?
What battery is installed: OEM or some other brand? Did you install the current battery? Rechargeable battery? Specs indicate a single AA battery for the wireless mouse version.
What did Evoluent actually say about the battery?
E.g., "Stop using the battery", "return battery and/or mouse for a replacement", etc...?
I would take a few photos of battery and mouse, send the photo's to Evoluent and request a refund/replacement as you desire.
Where did you purchase the mouse? How long ago? Seller? Any warranty left? RMA.
Keep records of all correspondence and anyone you talk with.
However, if the installed battery is some third party product then Evoluent is likely "out of the picture" and the warranty probably excludes damages from failed batteries.
In which case, if the mouse is working, then you will need to check the required battery specs and purchase the applicable replacement battery.