It depends on the workloads you subject it to. Except for extreme scenarios, you should be fine. Create a little clearance between the units and allow room for convection, don't put them in a cupboard.
If you are building a render farm out of new Mac mini's (don't), you're probably using them in a professional capacity. And you're probably planning to phase them out after 3-5 years. These are the kinds of scenarios where heat may be problematic.
If you plan to regularly max out the CPU and/or GPU of the unit (rendering, transcoding, gaming, heavy server loads), then two effects come into play:
- Thermal Throttling: Suboptimal performance, the CPU reduces its clock speed if it gets hotter.
The degree to which occurs depends on the design of the Mac mini's cooling solution. Some reviews indicate that the current model throttles during benchmarks and highly CPU-intensive workloads. Others indicate that it's not much of an issue.
- Reduced Lifespan: A Mac mini may die a little sooner if it is running hot continuously.
As stated by @lx07, the Mac mini will shut down if it gets too hot. However, this thermal protection only prevents the computer from burning out. Well before that point, the increase in temperature is likely to reduce both lifespan and reliability of electrical components.
Apple designs the thermal solution accordingly and buys sufficiently high-quality components that this should not generally be an issue. The fan in a MacBook Pro often does not kick in before it reaches 70c/158f. This is deliberate.
Do note that HDDs are more susceptible to heat. HDDs produce more heat than SSDs and are (in theory) more severely affected than other components because they rely on specific mechanical tolerances. BackBlaze keeps their drives very cool: mostly below 30c/86f. I'd expect the effect to be exacerbated above 50c/122f, but I can't find a good source. Drops and vibration are likely bigger contributors to HDD failure.