LED Intensity variation with Temperature (At constant Forward Current)?
LEDs intensity and chromaticity do deteriorate over time.  

This LED was designed in 1998 and when GaN LEDs were first being introduced.  It has horrific temperature stability.  A current blue LED will lose 10% max from 25°C to 150°C.

LEDs have come a long way in the past 20 years.  Use a newer lighting LED. 

I do not know enough about what you are doing with the LED to make any  recommendation.  

The best blue LEDs today are deep blue 450nm as they are used for most white LEDs and that is where the manufacturers R&amp;D goes.  

Update

For full spectrum you could use a white LED.  The white with the widest range I know of is the Luxeon Crisp White.  You would have to add IR and may have to add UV (Crisp White has a peak at 405nm).


LED engine, Lumiled, Cree, and OSRAM have Deep Blue to Far Red in their horticulture market.

LED Engine Inc. has some multi color LEDs 
Brochure: LuxiGen Brochure
They also have some interesting LEDs for Horiculture

The best option would be to make a custom PCB with all the available wavelength.  I would use OSRAM they have wavelengths 450 470 528 590 617 623 660 730.  OSRAM Horticulture Flyer
OSRAM Infrared Infrared LEDs

Lumileds has some new UV and IR: 
LUXEON IR Domed Line Product Datasheet
LUXEON UV U Line Product Datasheet
LUXEON UV FC Line Product Datasheet






  Can you suggest smaller LEDs?


Lumiled makes the smallest case (1.9mm x 1.9mm) LUXEON C Color Line Product Datasheet

There are only a few manufactures that make far red (≈720nm). When looking for LEDs with a wide spectrum, I first search for far red.  The target market for far red is horticulture which requires high power LEDs.  Very limited market.  

If by smaller you are looking for less power these LEDs can be driven with as little as 10mA.  Also the distance from the LED to the detector is a significant factor in radiated flux (inverse square law). 

To see what is available, you can do a parametric search on Digikey
 Digikey parametric search far red LEDs




  Can you suggest the LED covering IR range as much as possible?


LUXEON IR Domed Line Product Datasheet



The 860nm and 940nm are standard parts. If you need to fill in the valley at 880nm, these emitters are binned by wavelength. The problem is they are special order and you would likely have to buy a reel of them and wait 10 weeks.  





It would be difficult for me to chose LEDs for you as I do not know intensity and your other requirements. 

The other option to find what you need is by doing a Digikey search by wavelength. From this link choose the wavelength in the "wavelength" parameter column. Then sort the results by whatever parameter is most important. 

Digikey Infrared parametric search