I'd like to offer some technical facts to help allay fears and 'grandmother stories' about the risks/danger of using rechargeable batteries.
First, we assume we are talking about AA size (which is used by most flash units).
The standard AA battery is rated at 1.5V DC. Most flash units use 4 pcs in series, makes up 6V DC. This voltage is called the norminal voltage. As you use the flash, the energy in the batteries are consumed, and gradually, the voltage will drop. As this happens, the charging time for the flash unit will get longer and longer, until such time when the voltage becomes so low that it cannot charge the flash anymore. Then it's time to thrown them out and replace fresh ones.
There are 3 main types of 1.5V AA batteries; the manganese type, alkaline type, and lithium type. They all produce nominal 1.5V when new, and they all slow decrease through use. Lithium batteries lasts longest (but are more expensive), next is alkaline, then maganese type. As long as they are AA size with nominal 1.5V, it is OK to use in the flash unit.
Now comes to rechargeables. These normally have a nominal voltage of 1.2V. Many are made of Ni-MH. This offer high capacity and fast charging time for flash units (this is what we want right?). But 4 pcs of rechargeable at 1.2V each only adds up to 4.2V but the flash unit is designed to work with 6V. The law of electricity (too complicated to explain here) would then draw more current mA, due to the 1.2V shortfall, hence they may run a little hotter. The Nikon SB-800 compensates by allowing a 5th AA battery to be added on to the flash unit. Now 5 pcs of 1.2V rechargeable adds up to 6 volts, and we are back to what the flash unit is originally designed for.
With 5 pcs of 1.2V rechargeable batteries, and with their high capacity, charging time would be faster. With faster recycling time, more energy is dumped into the flash unit's capacitor, hence it will run somewhat hotter. So long as you work within the rated voltage and flash frequency as stated in your manual, you're ok.
Hope this note helps to allay fears and help some of you better understand.
Happy shooting.
Fred