Not really. Relays use only a fraction of a watt of power to operate, so the amount of heat they generate would hardly be noticeable.
Of course, in the engine bay, parts may get hot because of the engine heat, but I'm assuming you don't think that's a part of the problem you're describing.
Is this a single relay that's too hot, or the whole fusebox?
I can think of 3 reasons an individual relay might get hot on its own.
First, there might be too much load on the relay, beyond its rating, and the conductors inside are heating up. This might indicate wiring problems, or aftermarket devices that are drawing too much power.
Second, perhaps the contacts inside the relay are damaged with age and use, and are making poor contact. This would cause "resistive heating". This can occur naturally with use, or can be accelerated if there are large loads on that relay.
Third, the coil inside a relay may be failing and drawing more current than it's designed to. This also can occur with age.
If the whole fusebox is too hot (and it's not because of heat from an outside source), then either your alternator and battery voltages are low, or somehow you're drawing too much current through your electrical system. The latter problem can be caused by bad or deteriorating wiring, or the addition of too many or too large aftermarket devices to the system, such as large light systems or audio equipment. Large loads like those should be connected directly to the battery with their own independent fuse, relay (possibly), and wiring.
Why did you decide to check the relays in the first place?