Need to charge my logitech mouse, alternatively (electronics knowledge needed)

I purchased a fancy mouse from logitech, the The MX Revolution

As you can see, it’s around 100$. Not only do I sincerely love this mouse, it’s costly and I really don’t want to scrap it. The problem is that The charger for the mouse was left in a bag of mine which was stolen. Now, the mouse is dead and I’m looking to rig up something to be able to charge it. However, while I’m pretty crafty and knowledgable with electronics and soldering, I’m clueless with how charging works.

So, The charger is an upright design… pictured here

What can I do to rig up a makeshift carger? I opened the mouse and found a battery ((closely resembling a digital camera battery with +, _, and T terminals.

I’m unsure what the ‘T’ is for, what does this mean?

Further, the battery inside is 600mAh and 3.7V. It also states, ‘Limited charge voltage 4.2V’

What is a possible and safe way to rig up something to get a charge back into it?

(I know I can call logitech and ask for another… that’s plan B. I’ll be on the road for awhile and unable to accept delivery.)

Finally, the mouse has a rating of 4.1V== 800mA

I have all the additional information.
I appreciate all the help in advance and love electronic projects. How can I put a charge in my mouse???

You won’t be able to safely charge the batteries without an appropriate charger. You should try to order the new one now, and be resigned to using a cheap one until you get your charging base, if you can get one. Charging straight with a step down transformer will be a fire or explosion hazard.

I have a slightly different mouse but it looks like the same charger base. The base measures a DC output of 8.6 volts, positive on the right. The DC output from the wall wart is exactly the same so I’m suspecting the base is just pass-through wiring. Ohmic measurements seem to confirm this. I’d be comfortable rigging up a temporary DC supply for it, if it was my mouse.

That said, I agree with Harmonious and you should only jury-rig if you’re prepared to lose the mouse, and don’t leave alone it while it’s rigged-up.

Chargers for rechargable dry-cell batteries have microchips for precise control of the charge (to detect when the batteries have completed the charge), and for a very good reason (screwing this up causes fires). Unless you have a semiconductor lab in your basement I do not suggest building your own.