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The driving noise $\\dot W$ is a centered Gaussian generalized field that is fractional in time and has Riesz-type spatial covariance. For each fixed $x\\in\\mathbb R^d$, we establish a Khinchin-type law of the iterated logarithm at time zero for the temporal process $t\\mapsto u(t,x)$. 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The driving noise $\\dot W$ is a centered Gaussian generalized field that is fractional in time and has Riesz-type spatial covariance. For each fixed $x\\in\\mathbb R^d$, we establish a Khinchin-type law of the iterated logarithm at time zero for the temporal process $t\\mapsto u(t,x)$. 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