We study the speed at which nonglobal solutions to the fractional heat equation
u
t
+
(
−
Δ
)
α
/
2
u
=
u
p
,
\begin{equation*} u_t+(-\Delta )^{\alpha /2} u=u^p, \end{equation*}
with
0
>
α
>
2
0>\alpha >2
and
p
>
1
p>1
, tend to infinity. We prove that, assuming either
p
>
p
F
≡
1
+
α
/
N
p>p_F\equiv 1+\alpha /N
or
u
u
is strictly increasing in time, then for
t
t
close to the blow-up time
T
T
it holds that
‖
u
(
⋅
,
t
)
‖
∞
∼
(
T
−
t
)
−
1
p
−
1
\|u(\cdot ,t)\|_\infty \sim (T-t)^{-\frac 1{p-1}}
. The proofs use elementary tools, such as rescaling or comparison arguments.