Hot capacitors: Is that a problem?
I'll assume that these are power supply capacitors. 

Short answer: 


45C is tolerable. 
Cooler would be better. 
Taking steps to minimise temperature will improve lifetime, especially in a continuously on application.
All similarly specified capacitors are not created equal. Brand may matter.


Long! answer: 

That's hotter than you'd expect in a simple power supply circuit, but should be tolerable - but see below re operating lifetime that you can expect. "Rule of thumb" is that capacitor life halves for every 10 degrees C rise in temperature. If your capacitors are ~ 45C externally assume that the core is at say 55C. That's (105-55) = 50C lower than rated so lifetime will be about 2^5 = 32 times longer than nominal rating. Most capacitors (especially 105C rated ones) have a 2000 hour or better rating so you could expect a lifetime of about 2000 x 32 = 64000 hours or about 8 years of continuous operation. Even if core temperature was 65C that would give 4 years continuous. If the modem is run 24/7, as it may well be, then capacitor failure in the say 2 to 10 year timescale is not unexpected. What lifetime did you get from the original capacitors? And was the modem operated continuously?

Capacitors are also rated for "ripple current" and exceeding the ripple current rating will increase internal heating and reduce lifetime. This is an additive effect with temperature. eg If two capacitors are operating  at 50C then the one with a larger ripple current will have a shorter lifetime. Formulae are available to allow ripple current lifetime derating calculations (not to hand at present, I can provide if useful).

Ripple current ratings can vary widely between capacitor model and manufacturer. Using a known reputable brand of capacitor is recommended in demanding applications as specification sheets for unknown brands are often suspect, often having been copied from those of other manufacturers. [[This claim is based on my having personally tracked down the source of a significant number of data sheets of capacitors and other products when the claims did not seem to match reality. Internet searching on an unusual phrase will often allow the source to be located.]]

Operating your modem without its case is liable to reduce capacitor operating temperature and increase lifetime. Anything else you can sensibly do to reduce ambient temperature will also help. If you measure a 45C cap temperature in a 20C ambient room, if you then operate the modem in a 30C enclosure the cap temperature will probably be 55C or higher.

Fan cooling may make sense. But just replacing the caps when they fail or buying a new modem may be preferable. Heatsinks for capacitors are not unknown but are not common. Anything you can do to sensibly improve airflow will help. eg if it has no case then orientation may not matter much, so orienting it to improve air flow may be possible.

A datasheet or manufacturer's information should tell you


Rated operating temperature.
Lifetime at rated temperature.
Ripple current.
ESR (less commonly)


If they don't tell you the first three, buy another brand.
ESR is important but is reasonably well correlated with the other parameters. You can buy capacitors with 3000 hour or 5000 hour or even longer lifetimes at rated temperature, but cost is liable to be higher to much higher. You can buy capacitors with higher than 105C temperature ratings but they are usually much less common and probably expensive. 

There are many well known &amp; reputable brands. Panasonic make a wide range of grades, generally seem to "know their stuff" and often are not much dearer than little known or unknown brands. They are certainly not the only brand to consider but are a good starting place. 

Distributors like Digikey (www.digikey.com) stock a vast range of brands and models. Digikey have an excellent parametric search engine that allows you to selectively subset based on many different parameters. Even if you buy elsewhere their product search engine is a useful tool. Also see www.findchips.com 
[[No association with Panasonic or Digikey apart from being a satisfied user and customer/ database user.]]