Why and when do SSRs heat?
SSRs (solid state relays) are usually SCRs or triacs that are activated via a opto-coupler, all built into a single package.  One problem with triacs and SCRs is the voltage drop across them when on.  This can be 1.5 V or more.  Check the datasheet of the SCR you are using.  It should tell you the voltage drop.

Electrical power into a device is the current thru it times the voltage across it.  If the SSR drops 1.5 V and you're putting 10 A thru it, then it will dissipate 15 W.  Again, check the datasheet to see what kind of heat management might be required of this SSR.

There are SSRs that have lower voltage drop by using FETs, but these usually don't handle much current and are usually more expensive.

If you're not planning to switch often, then perhaps a mechanical relay might be more suitable.  These don't have one nice features of SCR and triac SCRs though, which is to turn off at the current zero-crossing.  That reduces emissions.

I know of one commercial product that used a SCR and relay in conjunction for switching AC line loads.  The SCR did the actual on and off switching, nicely synchronized to the AC zero crossings.  The relay did the heavy lifting by being turned on a little later and off a little earlier than the SCR.  The SCR therefore only dissipated power for a short time, and the relay never saw high switching stresses.  The lifetime tests suggested over 1 M switching cycles, something the relay would otherwise not have been good for.

To be clear, I'm not suggesting you do something like that.  I mention it to illustrate some of the properties of these things and how they have been harnessed and worked around in the past.