Do any other factors aside from length of input affect the runtime of the SHA-256 hashing algorithm?
Your question is not very clear, but I assume you're asking whether the runtime of a SHA-256 invocation depends on anything about the input other than its length. In other words, if an adversary knows how long it takes to calculate SHA-256(M1) and SHA-256(M2), does this leak any information about M1 and M2 other than their length?
The answer, with plausible implementations, is no. SHA-256 (like all common hash algorithms: MD5, SHA-1, SHA2, SHA3, Blake, etc.) only uses the message for bitwise operations (and, or, xor, shifts by a constant size, negation) and additions. All of these operations use a constant time on all common (and most imaginable) hardware, and compilers are very unlikely to turn them into non-constant-time operations. There are no multiplications or divisions (which on many CPU are not constant-time), no shifts by a message-dependent amount, no conditions or table lookups based on a value that's derived from the message content (other than the message's size).
So unlike, say, AES (where the most natural implementation involves a table lookup based on values derived from the key), you generally don't have to worry about timing-related side channels in SHA-256 or other common hash algorithms.
On the other hand, leaks from power consumption can be a worry.