I am working on a project in which I am using a Sparkfun Lithium Ion 850mAh battery https://www.sparkfun.com/products/13854
and wish to charge the battery via some solar cells.

I got some 5V 30mA (each) solar cells https://www.amazon.com/gp/product/B06XTS9SQ1/ref=oh_aui_detailpage_o01_s00?ie=UTF8&psc=1 and confirmed that they did indeed produce 30mA at 5V in full sun.

I had in my parts drawer a solar lipo charger from DFRobot which uses the CN3063 constant current/constant voltage linear charger IC https://www.dfrobot.com/product-1139.html The schematic is here http://image.dfrobot.com/image/data/DFR0264/Solar Charger V1.0 SCH.pdf.
The datasheet is here http://www.consonance-elec.com/pdf/datasheet/DSE-CN3063.pdf
Now the LiPo charger from DFRobot has tied the Temp input to GND and the battery is a 2-wire type, so it doesn't have a built-in thermistor.

The application is solar powered (charging) bicycle lights. So the battery is shielded from direct sun, but I expect there to be a reasonable amount of conductive heat from the bicycle frame and from the 3D printed case of the project to the battery. I looked over the datasheet https://cdn.sparkfun.com/datasheets/Prototyping/850mah-en-1.0ver.pdf
for the battery and saw that it has a charging temperature range of 0-45C.

What happens to the battery if it exceeds the 45C maximum temperature while charging? Will it explode/burn?

Is there a better type of battery for this kind of application?

 

NiMH are not popular, but far more stable than Li, and lighter and smaller than SLA.

I would definitely not use the battery you have, at or above that 45C and yes, fire is the likely failure mode, and a pretty violent fire at that. Explosion is a kinda relative term, and the specifics of your cell or battery would determine that, because accumulated pressure is key component of"explosion".

For applications where such heats exist and people are in proximity, SLA is probably the safest and most stable.