This is a common question we are asked and though it does depend on your application, typically you will need to use a heatsink.
Solid State Relays (SSRs) are designed to function at or within a specific temperature or range, temperatures outside this range can affect performance and shorten the overall life of the product. A proper heatsink will keep the SSR within the correct range to operate properly and will typically extend the life of the product. Most datasheets for SSRs will contain heatsink requirements and/or recommendations, so we highly recommend reviewing that information on the datasheet for your specific part.
In addition to heatsinking, it is important when designing the circuit to keep as much space as possible between your SSR and other parts that produce or operate at high temperatures.
For more information on heatsinks please see the below TechForum posts.